A218117 G.f.: A(x) = exp( Sum_{n>=1} A005261(n)*x^n/n ) where A005261(n) = Sum_{k=0..n} C(n,k)^5.

1, 2, 19, 198, 2961, 49566, 938322, 19083624, 412160478, 9305822076, 217855152321, 5251363667622, 129704365956114, 3269927116717728, 83893626609970281, 2185188966488265718, 57673989852987800966, 1539973309401567102832, 41544812360973818992909

Offset: 0

Author

Paul D. Hanna, Oct 21 2012

Keywords

• nonn

Comments

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

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

Examples

			G.f.: A(x) = 1 + 2*x + 19*x^2 + 198*x^3 + 2961*x^4 + 49566*x^5 + 938322*x^6 +...
log(A(x)) = 2*x + 34*x^2/2 + 488*x^3/3 + 9826*x^4/4 + 206252*x^5/5 + 4734304*x^6/6 + 113245568*x^7/7 +...+ A005261(n)*x^n/n +...
		

Crossrefs

Cf. A218115, A218118, A166990, A166992, A218119, A005261.

Programs

PARI

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

Formula

Equals row sums of triangle A218115.

Self-convolution of A218118.