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%I #22 Sep 14 2018 14:28:16
%S 1,1,2,9,22,115,576,2569,16780,100041,660220,4683811,36128544,
%T 279022627,2268178290,20870481675,183829795216,1733470364065,
%U 17049910933404,176955696148171,1863799931450200,19988658792216891,227401089360840802,2637188651044286923
%N "EGJ" (unordered, element, labeled) transform of 1,2,3,4,...
%H Vaclav Kotesovec, <a href="/A032315/b032315.txt">Table of n, a(n) for n = 0..400</a>
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%F E.g.f.: Product_{n>=1} (1 + x^n/n!)^n. - _Paul D. Hanna_, Nov 29 2010
%F 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
%o (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
%o (PARI) seq(n)={Vec(serlaplace(prod(k=1, n, (1 + x^k/k! + O(x*x^n))^k)))} \\ _Andrew Howroyd_, Sep 13 2018
%Y Cf. A174661.
%K nonn
%O 0,3
%A _Christian G. Bower_
%E a(0)=1 prepended and terms a(21) and beyond from _Andrew Howroyd_, Sep 13 2018
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