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

Author

Seiichi Manyama, Aug 08 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A374506, A375248, A375253.

Cf. A002426, A132885, A375259.

Programs

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))

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)).