A376835 Expansion of 1/((1-x)^4 - 8*x^4)^(1/4).

1, 1, 1, 1, 3, 11, 31, 71, 151, 343, 871, 2311, 6001, 15081, 37493, 94381, 241931, 625771, 1617211, 4164763, 10719793, 27674473, 71722773, 186353453, 484657729, 1260984161, 3283294561, 8559401761, 22343836711, 58391858383, 152722920691, 399719304411

Offset: 0

Author

Seiichi Manyama, Oct 06 2024

Keywords

• nonn

Crossrefs

Cf. A002426, A376836.

Cf. A004981.

Programs

Maple

f:= 1/((1-x)^4 - 8*x^4)^(1/4):
S:= series(f,x,41):
seq(coeff(S,x,i),i=0..40); # Robert Israel, Oct 06 2024

Mathematica

a[n_]:=Sum[(-8)^k * Binomial[-1/4,k] * Binomial[n,n-4*k],{k,0,Floor[n/4]}]; Array[a,32,0] (* Stefano Spezia, Oct 06 2024 *)

PARI

my(N=40, x='x+O('x^N)); Vec(1/((1-x)^4-8*x^4)^(1/4))

Formula

a(n) = Sum_{k=0..floor(n/4)} (-8)^k * binomial(-1/4,k) * binomial(n,n-4*k).

(7 + 7*n)*a(n) + (7 + 4*n)*a(n + 1) - (15 + 6*n)*a(n + 2) + (13 + 4*n)*a(n + 3) - (n + 4)*a(n + 4) = 0. - Robert Israel, Oct 06 2024