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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. 3
1, 0, 2, 36, 1012, 39344, 1999736, 128430272, 10191730992, 983072197248, 113716916603648, 15586891405986048, 2503750145139262912, 466531385595202181888, 99898407773515906674688, 24374095428098168225056256, 6724465905018382760077058816, 2083282714601993506101791682560, 720279202970620106946642875741696, 276363182440771615371629345051272192, 117079396081246222639524111231517394944 (list; graph; refs; listen; history; text; internal format)
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

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

Cf. A305597, A305598, A304861.

Sequence in context: A009539 A009554 A209036 * A210899 A302903 A259467

Adjacent sequences:  A305593 A305594 A305595 * A305597 A305598 A305599

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 05 2018

STATUS

approved

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Last modified May 7 18:29 EDT 2021. Contains 343652 sequences. (Running on oeis4.)