A206153 G.f.: exp( Sum_{n>=1} A206154(n)*x^n/n ), where A206154(n) = Sum_{k=0..n} binomial(n,k)^(k+2).

1, 2, 7, 48, 693, 26632, 2542514, 533442978, 278979307990, 343728261289376, 904762216681139381, 5771110378770242683658, 88742047516327429085056353, 2912737209806573079629325613400, 224604736339682169442980060945290802

Offset: 0

Author

Paul D. Hanna, Feb 04 2012

Keywords

• nonn

Comments

Logarithmic derivative yields A206154.

Examples

			G.f.: A(x) = 1 + 2*x + 7*x^2 + 48*x^3 + 693*x^4 + 26632*x^5 + 2542514*x^6 +...
where the logarithm of the g.f. begins:
log(A(x)) = 2*x + 10*x^2/2 + 110*x^3/3 + 2386*x^4/4 + 125752*x^5/5 + 14921404*x^6/6 +...+ A206154(n)*x^n/n +...
		

Crossrefs

Cf. A206154 (log), A184730, A206155, A206157, A206151.

Programs

PARI

{a(n)=polcoeff(exp(sum(m=1,n+1,x^m/m*sum(k=0,m,binomial(m,k)^(k+2))+x*O(x^n))),n)}
for(n=0,16,print1(a(n),", "))