A374513 Expansion of 1/(1 - 4*x - 4*x^2)^(7/2).

1, 14, 140, 1176, 8904, 62832, 421344, 2718144, 17008992, 103847744, 621292672, 3654187264, 21182563584, 121263109632, 686660004864, 3851149940736, 21416533501440, 118199459288064, 647926485764096, 3529938203545600, 19124354344775680

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(0) = 1, a(1) = 14; a(n) = (2*(2*n+5)*a(n-1) + 4*(n+5)*a(n-2))/n.

a(n) = (binomial(n+6,3)/20) * Sum_{k=0..floor(n/2)} 2^(n-k) * binomial(n+3,n-2*k) * binomial(2*k+3,k).

a(n) = 2^(n-4)*Pochhammer(n+1, 6)*hypergeom([(1-n)/2, -n/2], [4], 2)/45. - Stefano Spezia, Jul 10 2024

Mathematica

a[n_]:=2^(n-4) Pochhammer[n+1, 6]*Hypergeometric2F1[(1-n)/2, -n/2, 4, 2]/45; Array[a, 21, 0] (* Stefano Spezia, Jul 10 2024 *)

Prog

(PARI) a(n) = binomial(n+6, 3)/20*sum(k=0, n\2, 2^(n-k)*binomial(n+3, n-2*k)*binomial(2*k+3, k));

Crossrefs

Cf. A006139, A374497, A374511.

Sequence in context: A021044 A338323 A121034 * A125402 A016290 A003457

Adjacent sequences: A374510 A374511 A374512 * A374515 A374516 A374517

Keyword

nonn

Author

Seiichi Manyama, Jul 09 2024

Status

approved