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

Author

Paul D. Hanna, Jan 04 2011

Keywords

• nonn

Comments

Conjectured to consist entirely of integers.

Examples

			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 +...
		

Links

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

Crossrefs

Cf. A183240, A183239.

Programs

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)}

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