A110525 Expansion of 1/(1-x^2*c(3x)), c(x) the g.f. A000108.

1, 0, 1, 3, 19, 141, 1180, 10593, 99712, 971067, 9702388, 98899638, 1024429861, 10752006033, 114097140757, 1222113460332, 13195550763793, 143470913825427, 1569448022488435, 17261100136608984, 190752895126918819

Offset: 0

Author

Paul Barry, Jul 24 2005

Keywords

• easy
• nonn

Comments

Diagonal sums of A110518.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..930

Programs

Mathematica

Join[{1}, Table[Sum[(k/(n - k))*Binomial[2*n - 3*k - 1, n - 2*k]*3^(n - 2*k), {k, 0, Floor[n/2]}], {n, 1, 50}]] (* G. C. Greubel, Aug 30 2017 *)

PARI

concat([1], for(n=1,25, print1(sum(k=0,n\2, (k/(n - k))*binomial(2*n - 3*k - 1, n - 2*k)*3^(n - 2*k)), ", "))) \\ G. C. Greubel, Aug 30 2017

Formula

a(n) = Sum_{k=0..floor(n/2)} (k/(n-k))*C(2*n-3*k-1, n-2*k)*3^(n-2*k).