A305598 O.g.f. A(x) satisfies: 0 = [x^n] exp( n*(n-1) * x * A(x) ) / A(x), for n > 1, with A'(0) = 2.

1, 2, 6, 88, 2780, 116664, 6267112, 420608240, 34572479504, 3429310382112, 405606535944256, 56597546528049792, 9224898378261096640, 1739878267027277640320, 376408403518123974467840, 92655494325433865126295552, 25760341142562165894390054656, 8035192189219613566404655052288, 2794962730829750601921056190097920, 1078222968162147343121712468145172480

Offset: 0

Author

Paul D. Hanna, Jun 05 2018

Keywords

• nonn

Comments

It is remarkable that this sequence should consist entirely of integers.

Examples

			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 + ...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A305596, A305597.

Programs

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), ", "))

Formula

a(n) ~ c * n^(2*n + 2) / exp(2*n), where c = 29.852509905235658503543295008026... - Vaclav Kotesovec, Aug 11 2021