A181541 E.g.f.: A(x) = Product_{n>=1} (1 + x^n/n)^n.

1, 1, 2, 12, 54, 390, 3120, 28140, 290640, 3354960, 42561120, 586259520, 8806422240, 141680579040, 2446025662080, 44990666360640, 877867974023040, 18115179826423680, 394351821275892480, 9019730566889602560

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..444

Formula

E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*(-j)^(k-1))). - Ilya Gutkovskiy, Sep 12 2018

Example

E.g.f.: A(x) = 1 + x + 2*x^2/2! + 12*x^3/3! + 54*x^4/4! + 390*x^5/5! + ...
A(x) = (1+x)*(1 + x^2/2)^2*(1 + x^3/3)^3*(1 + x^4/4)^4*(1 + x^5/5)^5*...

Mathematica

nmax = 20; CoefficientList[Series[Product[(1+x^k/k)^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 07 2020 *)

Prog

(PARI) {a(n)=n!*polcoeff(prod(m=1, n, (1+x^m/m+x*O(x^n))^m), n)}

Crossrefs

Cf. A007838, A294469.

Sequence in context: A198150 A122676 A038175 * A197230 A025171 A375885

Adjacent sequences: A181538 A181539 A181540 * A181542 A181543 A181544

Keyword

nonn

Author

Paul D. Hanna, Nov 02 2010

Status

approved