A096047 a(n)=B(2n,4)/B(2n) (see comment).

1, 22, 346, 5482, 87466, 1398442, 22370986, 357919402, 5726644906, 91626056362, 1466015853226, 23456249457322, 375299974539946, 6004799525530282, 96076792140049066, 1537228673167043242, 24595658766377724586

Offset: 0

Author

Benoit Cloitre, Jun 17 2004

Keywords

• nonn
• easy

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

Links

• Index entries for linear recurrences with constant coefficients, signature (21,-84,64).

Crossrefs

Cf. A096045, A096046, A096048.

Programs

Mathematica

LinearRecurrence[{21,-84,64},{1,22,346},20] (* Harvey P. Dale, Oct 13 2016 *)

Maxima

a[0]:1$ a[1]:22$ a[2]:346$ a[n]:=(1/3)*(4*16^n+4^n-2)$ A096047(n):=a[n]$ makelist(A096047(n),n,0,30); /* Martin Ettl, Nov 13 2012 */

PARI

a(n)=sum(i=0,2*n,4^i*sum(j=0,i,binomial(2*n,j)*bernfrac(j)))/bernfrac(2*n)

Formula

a(n)=(1/3)*(4*16^n+4^n-2); a(0)=1, a(1)=22, a(2)=346 and a(n)=21*a(n-1)-84*a(n-2)+64*a(n-3)