OFFSET
0,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows
Peter Luschny, The Swiss-Knife polynomials.
FORMULA
Let c(k) = ((-1)^floor(k/4) / 2^floor(k/2)) * [4 not div k+1] (Iverson notation).
T(n,k) = Sum_{v=0..k} (-1)^v*binomial(k,v)*c(k)*(v+2)^n.
A155585(n) = Sum_{k=0..n} T(n,k).
EXAMPLE
Triangle begins:
1,
2, -1,
4, -5, 1,
8, -19, 9, 0,
16, -65, 55, 0, -6,
32, -211, 285, 0, -120, 30,
64, -665, 1351, 0, -1470, 810, -90,
128, -2059, 6069, 0, -14280, 13020, -3150, 0,
...
MAPLE
T := proc(n, k) local v, c; c := m -> if irem(m+1, 4) = 0 then 0 else 1/((-1)^iquo(m+1, 4)*2^iquo(m, 2)) fi; add((-1)^(v)*binomial(k, v)*c(k)*(v+2)^n, v=0..k) end: seq(print(seq(T(n, k), k=0..n)), n=0..8);
MATHEMATICA
c[m_] := If[Mod[m+1, 4] == 0, 0, 1/((-1)^Quotient[m+1, 4]*2^Quotient[m, 2])]; t[n_, k_] := Sum[(-1)^v*Binomial[k, v]*c[k]*(v+2)^n, {v, 0, k}]; Table[t[n, k], {n, 0, 7}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 30 2013, after Maple *)
CROSSREFS
KEYWORD
AUTHOR
Peter Luschny, Jan 07 2009
STATUS
approved