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A305596 O.g.f. A(x) satisfies: 0 = [x^n] exp( n*(n-1) * x * A(x) ) / A(x), for n > 0, with A'(0) = 0.

%I A305596 #16 Aug 11 2021 13:31:47
%S A305596 1,0,2,36,1012,39344,1999736,128430272,10191730992,983072197248,
%T A305596 113716916603648,15586891405986048,2503750145139262912,
%U A305596 466531385595202181888,99898407773515906674688,24374095428098168225056256,6724465905018382760077058816,2083282714601993506101791682560,720279202970620106946642875741696,276363182440771615371629345051272192,117079396081246222639524111231517394944
%N A305596 O.g.f. A(x) satisfies: 0 = [x^n] exp( n*(n-1) * x * A(x) ) / A(x), for n > 0, with A'(0) = 0.
%C A305596 It is remarkable that this sequence should consist entirely of integers.
%H A305596 Paul D. Hanna, <a href="/A305596/b305596.txt">Table of n, a(n) for n = 0..300</a>
%F A305596 a(n) ~ c * n^(2*n + 2) / exp(2*n), where c = 6.9180696045148043278035608619439... - _Vaclav Kotesovec_, Aug 11 2021
%e A305596 O.g.f.: A(x) = 1 + 2*x^2 + 36*x^3 + 1012*x^4 + 39344*x^5 + 1999736*x^6 + 128430272*x^7 + 10191730992*x^8 + 983072197248*x^9 + ...
%e A305596 RELATED SERIES.
%e A305596 A'(x)/A(x) = 4*x + 108*x^2 + 4040*x^3 + 196360*x^4 + 11982400*x^5 + 898207072*x^6 + 81486477600*x^7 + 8844334636032*x^8 + ...
%o A305596 (PARI) {a(n) = my(A=[1,0], 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 A305596 for(n=0, 20, print1(a(n), ", "))
%Y A305596 Cf. A305597, A305598, A304861.
%K A305596 nonn
%O A305596 0,3
%A A305596 _Paul D. Hanna_, Jun 05 2018