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%I A008502 #27 Sep 08 2022 08:44:35
%S A008502 1,10,55,220,715,2002,5005,11440,24310,48619,92368,167905,293710,
%T A008502 496705,815188,1302499,2031535,3100240,4638205,6814522,9847045,
%U A008502 14013220,19662655,27231610,37259596
%N A008502 8-dimensional centered tetrahedral numbers.
%H A008502 Bruno Berselli, <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL0EwMDg1MDIvYjAwODUwMi50eHQ">Table of n, a(n) for n = 0..1000</a>
%H A008502 <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL2luZGV4L1JlYyNvcmRlcl8wOQ">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1)
%F A008502 G.f.: (1-x^9 )/(1-x)^10 = (1+x+x^2)*(1+x^3+x^6) / (1-x)^9.
%F A008502 a(n) = 1 + n*(n+1)*(3*n^6+9*n^5+509*n^4+1003*n^3+11464*n^2+10964*n +36528)/13440. - _R. J. Mathar_, Nov 02 2011
%p A008502 seq(binomial(n+9,9)-binomial(n,9), n=0..30); # _G. C. Greubel_, Nov 09 2019
%t A008502 Table[Binomial[n + 9, 9] - Binomial[n, 9], {n, 0, 24}] (* _Bruno Berselli_, Mar 22 2012 *)
%t A008502 LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1}, {1,10,55,220,715,2002, 5005,11440,24310},30] (* _Harvey P. Dale_, Jan 17 2016 *)
%o A008502 (PARI) vector(31, n, b=binomial; b(n+8,9) - b(n-1,9) ) \\ _G. C. Greubel_, Nov 09 2019
%o A008502 (Magma) B:=Binomial; [B(n+9,9)-B(n,9): n in [0..30]]; // _G. C. Greubel_, Nov 09 2019
%o A008502 (Sage) b=binomial; [b(n+9,9)-b(n,9) for n in (0..30)] # _G. C. Greubel_, Nov 09 2019
%o A008502 (GAP) B:=Binomial;; List([0..30], n-> B(n+9,9)-B(n,9) ); # _G. C. Greubel_, Nov 09 2019
%K A008502 nonn,easy
%O A008502 0,2
%A A008502 _N. J. A. Sloane_

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