A387344 Expansion of 1/(1 - 8*x + 4*x^2)^(7/2).

1, 28, 490, 6888, 85134, 966504, 10329396, 105520272, 1040821782, 9982940968, 93584478988, 860746864432, 7790240975244, 69539700514704, 613370153844456, 5353909699803168, 46303471415495910, 397188087484393128, 3382162609845269404, 28610626973414978800

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..800

Formula

n*a(n) = 4*(2*n+5)*a(n-1) - 4*(n+5)*a(n-2) for n > 1.

a(n) = (binomial(n+6,3)/20) * A387340(n).

a(n) = (-1)^n * Sum_{k=0..n} (1/2)^(n-4*k) * binomial(-7/2,k) * binomial(k,n-k).

Mathematica

CoefficientList[Series[1/(1-8*x+4*x^2)^(7/2), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 28 2025 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(1/(1-8*x+4*x^2)^(7/2))
(Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/(1 - 8*x + 4*x^2)^(7/2); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // Vincenzo Librandi, Aug 28 2025

Crossrefs

Cf. A387340.

Sequence in context: A263949 A240463 A140107 * A028170 A211677 A076172

Adjacent sequences: A387341 A387342 A387343 * A387345 A387346 A387347

Keyword

nonn

Author

Seiichi Manyama, Aug 27 2025

Status

approved