A387283 Expansion of 1/((1-3*x) * (1-7*x))^(5/2).

1, 25, 385, 4725, 50820, 501900, 4672920, 41685600, 360085935, 3033805775, 25058420387, 203669422775, 1633497471060, 12955708250100, 101784012971220, 793140294780900, 6136733150696295, 47186865239460975, 360841077902101335, 2745899433121042275, 20804106874715457216

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..600

Formula

n*a(n) = (10*n+15)*a(n-1) - 21*(n+3)*a(n-2) for n > 1.

a(n) = (-1)^n * Sum_{k=0..n} 7^k * 3^(n-k) * binomial(-5/2,k) * binomial(-5/2,n-k).

a(n) = Sum_{k=0..n} (-4)^k * 3^(n-k) * binomial(-5/2,k) * binomial(n+4,n-k).

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

a(n) = (binomial(n+4,2)/6) * A387275(n).

a(n) = (-1)^n * Sum_{k=0..n} 10^k * (21/10)^(n-k) * binomial(-5/2,k) * binomial(k,n-k).

Mathematica

CoefficientList[Series[1/((1-3x)*(1-7*x))^(5/2), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 27 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/((1-3*x)*(1-7*x))^(5/2))
(Magma) R<x> := PowerSeriesRing(Rationals(), 34); f := 1/((1-3*x) * (1-7*x))^(5/2); coeffs := [ Coefficient(f, n) : n in [0..33] ]; coeffs; // Vincenzo Librandi, Aug 27 2025

Crossrefs

Cf. A387237, A387275.

Sequence in context: A387277 A228216 A261485 * A125482 A306322 A344733

Adjacent sequences: A387280 A387281 A387282 * A387284 A387285 A387286

Keyword

nonn

Author

Seiichi Manyama, Aug 24 2025

Status

approved