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

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

C. G. Bower, Transforms (2)

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

Prog

(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

Crossrefs

Cf. A174661.

Sequence in context: A091002 A330419 A025176 * A032224 A254710 A193758

Adjacent sequences: A032312 A032313 A032314 * A032316 A032317 A032318

Keyword

nonn

Author

Christian G. Bower

Extensions

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

Status

approved