A096048 a(n)=B(2n,6)/B(2n) (see comment).

1, 42, 1446, 51486, 1848966, 66524910, 2394568086, 86201542014, 3103229527206, 111716029897998, 4021774981740726, 144783880503964062, 5212219528644719046, 187639901505929327406, 6755036440486736068566

Offset: 0

Author

Benoit Cloitre, Jun 17 2004

Keywords

• nonn

Comments

B(n,p)=sum(i=0,n,p^i*sum(j=0,i,binomial(n,j)*B(j))) where B(k)=k-th Bernoulli number

Crossrefs

Cf. A096045, A096046, A096047.

Programs

Maxima

a[0]:1$ a[1]:42$ a[2]:1446$ a[3]:51486$ a[n]:=(1/10)*(11*36^n+2*9^n+3*4^n-6)$ A096048(n):=a[n]$ makelist(A096048(n),n,0,30); /* Martin Ettl, Nov 13 2012 */

PARI

a(n)=sum(i=0,2*n,6^i*sum(j=0,i,binomial(2*n,j)*bernfrac(j)))/bernfrac(2*n)

Formula

a(n)=(1/10)*(11*36^n+2*9^n+3*4^n-6); a(0)=1, a(1)=42, a(2)=1446, a(3)=51486 and a(n)=50*a(n-1)-553*a(n-2)+1800*a(n-3)-1296*a(n-4)