A136463 Diagonal of square array A136462: a(n) = C((n+1)*2^(n-1), n) for n>=0.

1, 2, 15, 560, 91390, 61124064, 163995687856, 1756185841659392, 75079359427627897200, 12831653340946454374300160, 8777916355714456994772455584000, 24054320541767107204031746600673906688

Offset: 0

Author

Paul D. Hanna, Dec 31 2007

Keywords

• nonn

Comments

a(n) is divisible by (n+1) for n>=0: a(n)/(n+1) = A136464(n).

Crossrefs

Cf. A136462; A136464; rows: A136465, A014070, A136466, A101346; A136467.

Programs

Mathematica

Table[Binomial[(n+1)2^(n-1),n],{n,0,15}]  (* Harvey P. Dale, Apr 20 2011 *)

PARI

a(n)=binomial((n+1)*2^(n-1),n)

PARI

/* a(n) = Coefficient of x^n in series: */
a(n)=polcoeff(sum(i=0,n,((n+1)/2)^i*log(1+2^i*x +x*O(x^n))^i/i!),n)

Formula

a(n) = [x^n] Sum_{i>=0} ((n+1)/2)^i * log(1 + 2^i*x)^i/i!.

a(n) is found in row n, column 0, of matrix power A136467^(n+1) for n>=0.

a(n) ~ exp(n+1) * 2^(n*(n-1)) / sqrt(2*Pi*n). - Vaclav Kotesovec, Jul 02 2016