

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.


5



1, 1, 3, 18, 213, 4128, 122638, 5096305, 284192429, 20375905738, 1829560187405, 200829815300994, 26471873341135571, 4124649654997542447, 750006492020987263020, 157382918361825037892997
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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(nk) for n>0 with a(0)=1.
a(n) ~ c * n! * (n1)!, where c = Product_{k>=2} 1/(11/(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, 1x^k/k!^2+O(x^(n+2)))))))), n)}


CROSSREFS

Cf. A183240, A183239.
Sequence in context: A157538 A024488 A217902 * A163883 A319580 A132727
Adjacent sequences: A183238 A183239 A183240 * A183242 A183243 A183244


KEYWORD

nonn


AUTHOR

Paul D. Hanna, Jan 04 2011


STATUS

approved



