A032315 "EGJ" (unordered, element, labeled) transform of 1,2,3,4,...

1, 1, 2, 9, 22, 115, 576, 2569, 16780, 100041, 660220, 4683811, 36128544, 279022627, 2268178290, 20870481675, 183829795216, 1733470364065, 17049910933404, 176955696148171, 1863799931450200, 19988658792216891, 227401089360840802, 2637188651044286923

Offset: 0

Author

Christian G. Bower

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..400
• C. G. Bower, Transforms (2)

Crossrefs

Cf. A174661.

Programs

PARI

{a(n)=n!*polcoeff(-1+prod(k=1,n,(1+x^k/k!+x*O(x^n))^k),n)} \\ Paul D. Hanna, Nov 29 2010

PARI

seq(n)={Vec(serlaplace(prod(k=1, n, (1 + x^k/k! + O(x*x^n))^k)))} \\ Andrew Howroyd, Sep 13 2018

Formula

E.g.f.: Product_{n>=1} (1 + x^n/n!)^n. - Paul D. Hanna, Nov 29 2010

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

Extensions

a(0)=1 prepended and terms a(21) and beyond from Andrew Howroyd, Sep 13 2018