A110521 Expansion of 1/(1 - (x + x^2)c(3x)), c(x) the g.f. of A000108.

1, 1, 5, 30, 224, 1871, 16771, 157668, 1533970, 15314626, 156008660, 1615147014, 16944659846, 179746651907, 1924700759635, 20776060271760, 225838715259574, 2469974866825150, 27160344857205806, 300101157823582668

Offset

0,3

Comments

Diagonal sums of A110519.

Links

G. C. Greubel, Table of n, a(n) for n = 0..925

Formula

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

Conjecture: 2*n*a(n) + 2*(16-11n)*a(n-1) + 2*(42-11n)*a(n-2) + (32-21n)*a(n-3) + 5*(20-7n)*a(n-4) + 6*(7-2n)*a(n-5) = 0. - R. J. Mathar, Dec 10 2011

Mathematica

T[0, 0] := 1; T[n_, k_] := Sum[j*3^(n - k - j)*Binomial[2*n - 2*k - j - 1, n - k - j]*Binomial[j, k]/(n - k), {j, 0, n - k}]; Table[Sum[T[n, k], {k, 0, Floor[n/2]}], {n, 0, 50}] (* G. C. Greubel, Aug 29 2017 *)

Prog

(PARI) concat([1], for(n=1, 20, print1(sum(k=0, n\2, sum(j=0, n-k, j*binomial(2*n-2*k-j-1, n-k-j)*binomial(j, k)*3^(n-k-j)/(n-k))), ", "))) \\ G. C. Greubel, Aug 29 2017

Crossrefs

Sequence in context: A137965 A371544 A129695 * A318920 A363908 A167892

Adjacent sequences: A110518 A110519 A110520 * A110522 A110523 A110524

Keyword

easy,nonn

Author

Paul Barry, Jul 24 2005

Status

approved