A218118 G.f.: A(x) = exp( Sum_{n>=1} A005261(n)/2*x^n/n ) where A005261(n) = Sum_{k=0..n} C(n,k)^5.

1, 1, 9, 90, 1350, 22623, 430338, 8786367, 190473510, 4314088755, 101271596421, 2446843690671, 60557118315384, 1529356193511525, 39297344717526330, 1024958399339092751, 27083985050402731646, 723942169622258974974, 19548657715769940178730

Offset

0,3

Comments

Compare to a g.f. of Catalan numbers (A000108):

exp( Sum_{n>=1} A000984(n)/2*x^n/n ) where A000984(n) = Sum_{k=0..n} C(n,k)^2.

Links

Table of n, a(n) for n=0..18.

Formula

Self-convolution equals A218117.

Example

 G.f.: A(x) = 1 + x + 9*x^2 + 90*x^3 + 1350*x^4 + 22623*x^5 + 430338*x^6 +...
log(A(x)) = x + 17*x^2/2 + 244*x^3/3 + 4913*x^4/4 + 103126*x^5/5 + 2367152*x^6/6 + 56622784*x^7/7 +...+ A005261(n)/2*x^n/n +...

Prog

 (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^5)/2*x^m/m)+x*O(x^n)), n)}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Cf. A218117, A166991, A166993, A218120, A005261.

Sequence in context: A062815 A294610 A294813 * A160569 A157545 A274953

Adjacent sequences: A218115 A218116 A218117 * A218119 A218120 A218121

Keyword

nonn

Author

Paul D. Hanna, Oct 21 2012

Status

approved