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A183239
G.f.: exp( Sum_{n>=1} A005651(n)*x^n/n ), where A005651 gives the sums of multinomial coefficients.
5
1, 1, 2, 5, 17, 69, 352, 2077, 14505, 114354, 1023839, 10130051, 110878314, 1320375213, 17086334702, 237832320231, 3552995476517, 56590659564489, 958653346775294, 17192978984630744, 325681548343314833, 6494280460641306608
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * (n-1)!, where c = Product_{k>=2} 1/(1-1/k!) = A247551 = 2.52947747207915264... . - Vaclav Kotesovec, Feb 19 2015
EXAMPLE
G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 17*x^4 + 69*x^5 + 352*x^6 +...
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 +...
PROG
(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)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 03 2011
STATUS
approved