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

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

Vaclav Kotesovec, Table of n, a(n) for n = 0..420

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

Cf. A005651, A183238, A183241.

Sequence in context: A162037 A319467 A326412 * A263639 A263679 A251177

Adjacent sequences: A183236 A183237 A183238 * A183240 A183241 A183242

Keyword

nonn

Author

Paul D. Hanna, Jan 03 2011

Status

approved