%I #13 Oct 21 2022 22:04:30
%S 1,22,346,5482,87466,1398442,22370986,357919402,5726644906,
%T 91626056362,1466015853226,23456249457322,375299974539946,
%U 6004799525530282,96076792140049066,1537228673167043242,24595658766377724586
%N a(n)=B(2n,4)/B(2n) (see comment).
%C 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
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-84,64).
%F 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)
%t LinearRecurrence[{21,-84,64},{1,22,346},20] (* _Harvey P. Dale_, Oct 13 2016 *)
%o (PARI) a(n)=sum(i=0,2*n,4^i*sum(j=0,i,binomial(2*n,j)*bernfrac(j)))/bernfrac(2*n)
%o (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 */
%Y Cf. A096045, A096046, A096048.
%K nonn,easy
%O 0,2
%A _Benoit Cloitre_, Jun 17 2004