A182963 G.f.: A(x) = exp( Sum_{n>=1} A183235(n)*x^n/n ) where A183235 is the sums of the cubes of multinomial coefficients.

1, 1, 5, 86, 4052, 400401, 71827456, 21068995258, 9429303819612, 6105894632883407, 5493030296624140330, 6644655430011095138676, 10523095865317003368417750, 21337870239129956669159151372

Offset: 0

Author

Paul D. Hanna, Jan 04 2011

Keywords

• nonn

Comments

Conjectured to consist entirely of integers.

Examples

			G.f.: A(x) = 1 + x + 5*x^2 + 86*x^3 + 4052*x^4 + 400401*x^5 +...
log(A(x)) = x + 9*x^2/2 + 244*x^3/3 + 15833*x^4/4 + 1980126*x^5/5 + 428447592*x^6/6 + 146966837193*x^7/7 +...+ A183235(n)*x^n/n +...
		

Crossrefs

Cf. A183235, A183239, A183241.

Programs

PARI

{a(n)=polcoeff(exp(intformal(1/x*(-1+serlaplace(serlaplace(serlaplace(1/prod(k=1, n+1, 1-x^k/k!^3+O(x^(n+2))))))))), n)}

Formula

a(n) = (1/n)*Sum_{k=1..n} A183235(k)*a(n-k) for n>0 with a(0)=1.