OFFSET
0,2
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 = 29.852509905235658503543295008026... - Vaclav Kotesovec, Aug 11 2021
EXAMPLE
O.g.f.: A(x) = 1 + 2*x + 6*x^2 + 88*x^3 + 2780*x^4 + 116664*x^5 + 6267112*x^6 + 420608240*x^7 + 34572479504*x^8 + 3429310382112*x^9 + ...
RELATED SERIES.
A'(x)/A(x) = 2 + 8*x + 236*x^2 + 10424*x^3 + 554792*x^4 + 36154208*x^5 + 2853579584*x^6 + 269659065120*x^7 + 30227424970304*x^8 + ...
PROG
(PARI) {a(n) = my(A=[1, 2], 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