A183241 G.f.: A(x) = exp( Sum_{n>=1} A183240(n)*x^n/n ) where A183240 is the sums of the squares of multinomial coefficients.

1, 1, 3, 18, 213, 4128, 122638, 5096305, 284192429, 20375905738, 1829560187405, 200829815300994, 26471873341135571, 4124649654997542447, 750006492020987263020, 157382918361825037892997

Offset

0,3

Comments

Conjectured to consist entirely of integers.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..250

Formula

a(n) = (1/n)*Sum_{k=1..n} A183240(k)*a(n-k) for n>0 with a(0)=1.

a(n) ~ c * n! * (n-1)!, where c = Product_{k>=2} 1/(1-1/(k!)^2) = 1.37391178018464563291... . - Vaclav Kotesovec, Feb 19 2015

Example

G.f.: A(x) = 1 + x + 3*x^2 + 18*x^3 + 213*x^4 + 4128*x^5 +...
log(A(x)) = x + 5*x^2/2 + 46*x^3/3 + 773*x^4/4 + 19426*x^5/5 + 708062*x^6/6 + 34740805*x^7/7 +...+ A183240(n)*x^n/n +...

Prog

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

Crossrefs

Cf. A183240, A183239.

Sequence in context: A024488 A217902 A356614 * A163883 A319580 A132727

Adjacent sequences: A183238 A183239 A183240 * A183242 A183243 A183244

Keyword

nonn

Author

Paul D. Hanna, Jan 04 2011

Status

approved