A218119 G.f.: A(x) = exp( Sum_{n>=1} A069865(n)*x^n/n ) where A069865(n) = Sum_{k=0..n} C(n,k)^6.

1, 2, 35, 554, 15297, 451842, 15929824, 601077640, 24488754772, 1046792248856, 46718718597567, 2155032002133834, 102259392504591235, 4967499746642163574, 246231868462969357492, 12419324761881256326288, 635990044563649443993091, 33006906229799699591298070

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 + 35*x^2 + 554*x^3 + 15297*x^4 + 451842*x^5 + 15929824*x^6 +...
log(A(x)) = 2*x + 66*x^2/2 + 1460*x^3/3 + 54850*x^4/4 + 2031252*x^5/5 + 86874564*x^6/6 + 3848298792*x^7/7 +...+ A069865(n)*x^n/n +...
		

Crossrefs

Cf. A218116, A218120, A166990, A166992, A218117, A069865.

Programs

PARI

{a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^6)*x^m/m)+x*O(x^n)), n)}
for(n=0,25,print1(a(n),", "))

Formula

Equals row sums of triangle A218116.

Self-convolution of A218120.