|
|
A096047
|
|
a(n)=B(2n,4)/B(2n) (see comment).
|
|
10
|
|
|
1, 22, 346, 5482, 87466, 1398442, 22370986, 357919402, 5726644906, 91626056362, 1466015853226, 23456249457322, 375299974539946, 6004799525530282, 96076792140049066, 1537228673167043242, 24595658766377724586
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
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
|
|
|
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)
|
|
MATHEMATICA
|
LinearRecurrence[{21, -84, 64}, {1, 22, 346}, 20] (* Harvey P. Dale, Oct 13 2016 *)
|
|
PROG
|
(PARI) a(n)=sum(i=0, 2*n, 4^i*sum(j=0, i, binomial(2*n, j)*bernfrac(j)))/bernfrac(2*n)
(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 */
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|