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A372200 E.g.f. A(x) satisfies A(x) = exp( 2 * x / (1 - x * A(x)^(1/2))^2 ). 2
1, 2, 12, 116, 1600, 28832, 643864, 17190392, 534707296, 19003345568, 760054943464, 33798503960168, 1654577248619728, 88437537019736816, 5125378381513865752, 320163561707158120568, 21445740148760729672896, 1533498858453023915309888 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A161635.
If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s ), then a(n) = r * n! * Sum_{k=0..n} (t*k+u*(n-k)+r)^(k-1) * binomial(n+(s-1)*k-1,n-k)/k!.
PROG
(PARI) a(n, r=2, s=2, t=0, u=1) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(n+(s-1)*k-1, n-k)/k!);
CROSSREFS
Sequence in context: A035051 A214222 A227459 * A290840 A012628 A012623
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 21 2024
STATUS
approved

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Last modified June 15 19:43 EDT 2024. Contains 373410 sequences. (Running on oeis4.)