A177411 a(n) = binomial((n+1)*2^(n+1), n)/(n+1).

1, 4, 92, 10416, 5258872, 11297164096, 100955979001152, 3709635244861142784, 556796318904269731012544, 339945532169833436692992549888, 841788571395046141591475043524725760

Offset: 0

Author

Paul D. Hanna, Jun 26 2010

Keywords

• nonn

Crossrefs

Cf. A177410, A177400.

Programs

Mathematica

Table[Binomial[(n+1)2^(n+1),n]/(n+1),{n,0,20}] (* Harvey P. Dale, Feb 03 2019 *)

PARI

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

PARI

{a(n)=polcoeff(sum(k=0, n, 2^k*(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+1))/(n+1).

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