A375260 Expansion of (1 - 3*x + 9*x^2 - 7*x^3)/(1 - 2*x - 3*x^2)^(7/2).

1, 4, 30, 140, 665, 2856, 11844, 47160, 182655, 690580, 2560558, 9337692, 33573995, 119246960, 419034360, 1458687312, 5035531563, 17253821340, 58723235970, 198655153620, 668338862499, 2237229875496, 7454611712100, 24734393119800, 81748883914425

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

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

a(n) = binomial(n+3,3) * A002426(n).

a(n) = A132885(n+6,3).

a(n) = ((n+3)/n^2) * ((2*n-1)*a(n-1) + 3*(n+2)*a(n-2)).

a(n) ~ 3^(n-1/2) * n^(5/2) / (4 * sqrt(Pi)). - Amiram Eldar, Dec 02 2025

Mathematica

a[n_] := Binomial[n + 3, 3] * GegenbauerC[n, -n, -1/2]; a[0] = 1; Array[a, 30, 0] (* Amiram Eldar, Dec 02 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec((1-3*x+9*x^2-7*x^3)/(1-2*x-3*x^2)^(7/2))

Crossrefs

Cf. A374506, A375248, A375253.

Cf. A002426, A132885, A375259.

Sequence in context: A005715 A281950 A316178 * A305764 A317113 A123351

Adjacent sequences: A375257 A375258 A375259 * A375261 A375262 A375263

Keyword

nonn

Author

Seiichi Manyama, Aug 08 2024

Status

approved