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

0,4

Comments

Diagonal sums of A110518.

Links

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

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).

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 *)

Prog

(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

Crossrefs

Sequence in context: A025571 A221266 A082758 * A331716 A058859 A291964

Adjacent sequences: A110522 A110523 A110524 * A110526 A110527 A110528

Keyword

easy,nonn

Author

Paul Barry, Jul 24 2005

Status

approved