A387238 Expansion of 1/((1-x) * (1-5*x))^(7/2).

1, 21, 266, 2646, 22806, 178794, 1310694, 9140274, 61330269, 399107709, 2533330800, 15751925280, 96257031780, 579556206180, 3445117599480, 20252115155160, 117890464642335, 680320688005035, 3895668955041710, 22152779612619810, 125183331416173030

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Formula

n*a(n) = (6*n+15)*a(n-1) - 5*(n+5)*a(n-2) for n > 1.

a(n) = (-1)^n * Sum_{k=0..n} 5^k * binomial(-7/2,k) * binomial(-7/2,n-k).

a(n) = Sum_{k=0..n} (-4)^k * binomial(-7/2,k) * binomial(n+6,n-k).

a(n) = Sum_{k=0..n} 4^k * 5^(n-k) * binomial(-7/2,k) * binomial(n+6,n-k).

a(n) = (binomial(n+6,3)/20) * A387239(n).

a(n) = (-1)^n * Sum_{k=0..n} 6^k * (5/6)^(n-k) * binomial(-7/2,k) * binomial(k,n-k).

Mathematica

CoefficientList[Series[1/((1-x)*(1-5*x))^(7/2), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 24 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/((1-x)*(1-5*x))^(7/2))
(Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/((1-x) * (1-5*x))^(7/2); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // Vincenzo Librandi, Aug 24 2025

Crossrefs

Cf. A026375, A385563, A387237.

Cf. A126190, A374509, A387239.

Sequence in context: A169895 A092794 A133717 * A056282 A000770 A327507

Adjacent sequences: A387235 A387236 A387237 * A387239 A387240 A387241

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2025

Status

approved