The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A008495

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A008495

Expansion of (1-x^13) / (1-x)^13.
(history; published version)

#28 by Charles R Greathouse IV at Thu Sep 08 08:44:35 EDT 2022

PROG

(MAGMAMagma) [1] cat [13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800: n in [1..40]]; // G. C. Greubel, Nov 07 2019

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#27 by Susanna Cuyler at Fri Nov 08 05:59:10 EST 2019

STATUS

reviewed

approved

#26 by Michel Marcus at Fri Nov 08 00:40:50 EST 2019

STATUS

proposed

reviewed

#25 by G. C. Greubel at Thu Nov 07 23:56:52 EST 2019

STATUS

editing

proposed

#24 by G. C. Greubel at Thu Nov 07 23:56:47 EST 2019

FORMULA

a(n) = 13*(n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10))/39916800 for n>0.

G.f.: (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12) / (1 - x)^12. (End)

(End)

E.g.f.: 1 + x*(518918400 +1297296000*x +1470268800*x^2 +821620800*x^3 + 263783520*x^4 +51171120*x^5 +6280560*x^6 +489060*x^7 +24310*x^8 + 715*x^9 +13*x^10)*exp(x)/39916800. - G. C. Greubel, Nov 07 2019

MAPLE

1, seq(13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800, n=1..40); # G. C. Greubel, Nov 07 2019

MATHEMATICA

CoefficientList[(1 - x^13)/(1 - x)^13 + O[x]^30, x] (* Jean-François Alcover, Jan 09 2019 *)

Table[If[n==0, 1, 13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800], {n, 0, 40}] (* G. C. Greubel, Nov 07 2019 *)

PROG

(MAGMA) [1] cat [13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800: n in [1..40]]; // G. C. Greubel, Nov 07 2019

(Sage) [1]+[13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800 for n in (1..40)] # G. C. Greubel, Nov 07 2019

(GAP) Concatenation([1], List([1..40], n-> 13*n*(19056960 + 18128396*n^2 + 2641925*n^4 + 88803*n^6 + 715*n^8 + n^10)/39916800 )); # G. C. Greubel, Nov 07 2019

STATUS

approved

editing

#23 by Bruno Berselli at Wed Jan 09 03:32:24 EST 2019

STATUS

proposed

approved

#22 by Michel Marcus at Wed Jan 09 03:13:52 EST 2019

STATUS

editing

proposed

#21 by Michel Marcus at Wed Jan 09 03:13:47 EST 2019

LINKS

M. Beck and S. Hosten, <a href="http://arxiv.org/abs/math/0508136">Cyclotomic polytopes and growth series of cyclotomic lattices</a>, arXiv :math.CO/0508136, [math.CO], 2005-2006.

STATUS

proposed

editing

#20 by Jean-François Alcover at Wed Jan 09 03:09:28 EST 2019

STATUS

editing

proposed

#19 by Jean-François Alcover at Wed Jan 09 03:09:23 EST 2019

MATHEMATICA

CoefficientList[(1 - x^13)/(1 - x)^13 + O[x]^30, x] (* Jean-François Alcover, Jan 09 2019 *)

STATUS

approved

editing