A152600 a(n)=0^n+sum{k=0..n-1, C(n+k-1,2k)*A000108(k)*3^k*2^(n-k)}.

1, 2, 10, 80, 790, 8720, 103060, 1275680, 16326190, 214280720, 2868504460, 39014154080, 537592643740, 7488960021920, 105295566289960, 1492291482505280, 21296015905884190, 305755507155234320

Offset: 0

Author

Paul Barry, Dec 09 2008

Keywords

• easy
• nonn

Comments

Hankel transform is 2^n*3^C(n+1,2)*5^C(n,2). A152601(n)=a(n+1)/2.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Programs

Mathematica

Flatten[{1,2,Table[2^n*(4*(n+1)*LegendreP[n+1,4]-(31*n+16)*LegendreP[n,4])/(3*n*(n-1)),{n,2,20}]}] (* Vaclav Kotesovec, Oct 20 2012 *)

PARI

a(n)=if(n>1, (4*(n+1)*pollegendre(n+1,4) - (31*n+16)*pollegendre(n,4))/(3*n*(n-1))<Charles R Greathouse IV, Mar 19 2017

Formula

a(n) = 2^n * (4*(n+1)*LegendreP(n+1,4) - (31*n+16)*LegendreP(n,4))/(3*n*(n-1)) for n>1. - Mark van Hoeij, May 27 2010

Recurrence: n*a(n) = 8*(2*n-3)*a(n-1) - 4*(n-3)*a(n-2). - Vaclav Kotesovec, Oct 20 2012

a(n) ~ sqrt(8*sqrt(15)-30)*(8+2*sqrt(15))^n/(6*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 20 2012