A376836 Expansion of 1/((1-x)^8 - 16*x^8)^(1/8).
1, 1, 1, 1, 1, 1, 1, 1, 3, 19, 91, 331, 991, 2575, 6007, 12871, 25759, 48927, 90271, 168607, 339151, 773263, 1982575, 5393455, 14709625, 38941801, 98802081, 239718961, 557984701, 1254360781, 2750444101, 5961934261, 12986219371, 28897996843, 66459189259, 158256566091
Offset: 0
Keywords
Programs
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Mathematica
a[n_]:=Sum[(-16)^k * Binomial[-1/8,k] * Binomial[n,n-8*k],{k,0,Floor[n/8]}]; Array[a,36,0] (* Stefano Spezia, Oct 06 2024 *) -
PARI
my(N=40, x='x+O('x^N)); Vec(1/((1-x)^8-16*x^8)^(1/8))
Formula
a(n) = Sum_{k=0..floor(n/8)} (-16)^k * binomial(-1/8,k) * binomial(n,n-8*k).