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A183239 G.f.: exp( Sum_{n>=1} A005651(n)*x^n/n ), where A005651 gives the sums of multinomial coefficients.

%I A183239 #9 Feb 19 2015 15:29:57
%S A183239 1,1,2,5,17,69,352,2077,14505,114354,1023839,10130051,110878314,
%T A183239 1320375213,17086334702,237832320231,3552995476517,56590659564489,
%U A183239 958653346775294,17192978984630744,325681548343314833,6494280460641306608
%N A183239 G.f.: exp( Sum_{n>=1} A005651(n)*x^n/n ), where A005651 gives the sums of multinomial coefficients.
%H A183239 Vaclav Kotesovec, <a href="/A183239/b183239.txt">Table of n, a(n) for n = 0..420</a>
%F A183239 a(n) ~ c * (n-1)!, where c = Product_{k>=2} 1/(1-1/k!) = A247551 = 2.52947747207915264... . - _Vaclav Kotesovec_, Feb 19 2015
%e A183239 G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 17*x^4 + 69*x^5 + 352*x^6 +...
%e A183239 log(A(x)) = x + 3*x^2/2 + 10*x^3/3 + 47*x^4/4 + 246*x^5/5 + 1602*x^6/6 + 11481*x^7/7 + 95503*x^8/8 +...+ A005651(n)*x^n/n +...
%o A183239 (PARI) {a(n)=polcoeff(exp(intformal(1/x*(-1+serlaplace(1/prod(k=1,n+1,1-x^k/k!+O(x^(n+2))))))),n)}
%Y A183239 Cf. A005651, A183238, A183241.
%K A183239 nonn
%O A183239 0,3
%A A183239 _Paul D. Hanna_, Jan 03 2011