OFFSET
0,3
COMMENTS
It is remarkable that this sequence should consist entirely of integers.
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..300
FORMULA
a(n) ~ c * n^(2*n + 2) / exp(2*n), where c = 6.9180696045148043278035608619439... - Vaclav Kotesovec, Aug 11 2021
EXAMPLE
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 + ...
RELATED SERIES.
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 + ...
PROG
(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]}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 05 2018
STATUS
approved