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%I #17 Aug 11 2021 13:36:47
%S 1,1,3,59,1775,71511,3735265,245211865,19803108233,1936950231585,
%T 226553844824131,31331105054010115,5069552336811706983,
%U 950370245531340684983,204551803567400710962529,50129834142929585060592433,13883636379729966042468837937,4315912911594085891292265635265,1496719856496801168910452641821123,575834703501821334832940981183532907
%N O.g.f. A(x) satisfies: 0 = [x^n] exp( n*(n-1) * x * A(x) ) / A(x), for n > 1, with A'(0) = 1.
%C It is remarkable that this sequence should consist entirely of integers.
%H Paul D. Hanna, <a href="/A305597/b305597.txt">Table of n, a(n) for n = 0..300</a>
%F a(n) ~ c * n^(2*n + 2) / exp(2*n), where c = 15.159858073932625358279885219043... - _Vaclav Kotesovec_, Aug 11 2021
%e O.g.f.: A(x) = 1 + x + 3*x^2 + 59*x^3 + 1775*x^4 + 71511*x^5 + 3735265*x^6 + 245211865*x^7 + 19803108233*x^8 + 1936950231585*x^9 + ...
%e RELATED SERIES.
%e A'(x)/A(x) = 1 + 5*x + 169*x^2 + 6857*x^3 + 348121*x^4 + 21952541*x^5 + 1688688793*x^6 + 156361635585*x^7 + 17247060489337*x^8 + ...
%o (PARI) {a(n) = my(A=[1,1], m); for(i=1, n+1, m=#A; A=concat(A, 0); A[m+1] = Vec( exp(m*(m-1)*x*Ser(A)) / Ser(A) )[m+1] ); A[n+1]}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A305596, A305598.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jun 05 2018
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