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

0,3

Comments

Conjectured to consist entirely of integers.

Links

Table of n, a(n) for n=0..13.

Formula

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

Example

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 +...

Prog

(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)}

Crossrefs

Cf. A183235, A183239, A183241.

Sequence in context: A243075 A232489 A318219 * A220617 A231702 A069948

Adjacent sequences: A182960 A182961 A182962 * A182964 A182965 A182966

Keyword

nonn

Author

Paul D. Hanna, Jan 04 2011

Status

approved