A209902 E.g.f.: Product_{n>=1} 1/(1 - x^n)^(1/n!).

1, 1, 3, 10, 50, 261, 1877, 13511, 122663, 1150988, 12656562, 142842855, 1882666887, 24961232401, 375233443223, 5784328028680, 98433762560780, 1704971188321787, 32593405802749763, 629093184347294419, 13243913786996162915, 283647771230983625422

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Formula

E.g.f.: exp( Sum_{n>=1} (exp(x^n) - 1)/n ).

E.g.f.: exp( Sum_{n>=1} A087906(n)*x^n/n! ) where A087906(n) = Sum_{d|n} (n-1)!/(d-1)!.

E.g.f.: Product_{n>=1} B(x^n)^(1/n) where B(x) = exp(exp(x)-1) = e.g.f. of Bell numbers.

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 10*x^3/3! + 50*x^4/4! + 261*x^5/5! +...
such that
A(x) = 1/((1-x) * (1-x^2)^(1/2) * (1-x^3)^(1/3!) * (1-x^4)^(1/4!) *...).

Prog

(PARI) {a(n)=n!*polcoeff(prod(m=1, n, 1/(1-x^m+x*O(x^n))^(1/m!)), n)}
for(n=0, 21, print1(a(n), ", "))

Crossrefs

Cf. A087906.

Sequence in context: A297295 A088142 A276028 * A049370 A009343 A352414

Adjacent sequences: A209899 A209900 A209901 * A209903 A209904 A209905

Keyword

nonn

Author

Paul D. Hanna, Mar 14 2012

Status

approved