A177410 a(n) = binomial((n+1)*2^n, n)/(n+1).

1, 2, 22, 1240, 316316, 343855008, 1551088459936, 28684932916796288, 2161788213413182113760, 661624062463590275090838016, 820418024446932078541699530057216

Offset: 0

Author

Paul D. Hanna, Jun 26 2010

Keywords

• nonn

Crossrefs

Cf. A177411, A177400.

Programs

PARI

{a(n)=binomial((n+1)*2^n,n)/(n+1)}

PARI

{a(n)=polcoeff(sum(k=0, n, (n+1)^(k-1)*log(1+2^k*x +x*O(x^n))^k/k!), n)} \\ Paul D. Hanna, Jul 03 2010

Formula

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

a(n) = [x^n] Sum_{k=0..n} (n+1)^(k-1) * log(1 + 2^k*x)^k/k!. - Paul D. Hanna, Jul 03 2010