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A032315 "EGJ" (unordered, element, labeled) transform of 1,2,3,4,... 5
1, 1, 2, 9, 22, 115, 576, 2569, 16780, 100041, 660220, 4683811, 36128544, 279022627, 2268178290, 20870481675, 183829795216, 1733470364065, 17049910933404, 176955696148171, 1863799931450200, 19988658792216891, 227401089360840802, 2637188651044286923 (list; graph; refs; listen; history; text; internal format)
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: A319792 A091002 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

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Last modified October 20 15:03 EDT 2018. Contains 316388 sequences. (Running on oeis4.)