A370104 a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n+k-1,k) * binomial(6*n-k-1,n-k).

1, 3, 25, 219, 2025, 19253, 186469, 1829565, 18124521, 180886260, 1815946275, 18318160358, 185518492965, 1885157971596, 19211066004995, 196258973605094, 2009302383218409, 20610411795602760, 211768072490024440, 2179156980022097775, 22454554231950998275

Offset

0,2

Links

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

Formula

a(n) = [x^n] 1/( (1+x)^2 * (1-x)^5 )^n.

The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x*(1+x)^2*(1-x)^5 ). See A365856.

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

Prog

(PARI) a(n) = sum(k=0, n, (-1)^k*binomial(2*n+k-1, k)*binomial(6*n-k-1, n-k));
(PARI) a(n, s=2, t=2, u=3) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial((u+1)*n-s*k-1, n-s*k));

Crossrefs

Cf. A351857, A370103.

Cf. A365856.

Sequence in context: A230718 A112240 A155640 * A024217 A199679 A118726

Adjacent sequences: A370101 A370102 A370103 * A370105 A370106 A370107

Keyword

nonn

Author

Seiichi Manyama, Feb 10 2024

Status

approved