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A338377 G.f. satisfies: A(x) = (1 + x * d/dx(x*A(x)) )^n. 3
1, 1, 9, 226, 10745, 811026, 88058362, 12920344256, 2453913830097, 584608650175630, 170543970449421371, 59769169004510011674, 24775053368568412720967, 11989194513429991057937296, 6698670769128767044654361520, 4280089524780608663200103685056, 3101341801862271814724389007080481 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..220

FORMULA

G.f. satisfies: A(x) = (1 + x * A(x) + x^2 * A'(x) )^n.

a(n) ~ A238223 * exp(1) * n! * n^(n + 1 - 1/n).

a(n) ~ A238223 * exp(1) * n^(n+1) * n! * (1 - log(n)/n).

EXAMPLE

a(2) = A113662(2) = 9

a(3) = A113663(3) = 226

a(4) = A113664(4) = 10745

a(5) = A113665(5) = 811026

a(6) = A113666(6) = 88058362

a(7) = A113667(7) = 12920344256

a(8) = A113668(8) = 2453913830097

PROG

(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=1, n, A=(1+x*deriv(x*A))^n); polcoeff(A, n, x)}

for(n=0, 20, print1(a(n), ", "))

CROSSREFS

Cf. A113662, A113663, A113664, A113665, A113666, A113667, A113668.

Sequence in context: A285985 A330830 A218536 * A211048 A327146 A158728

Adjacent sequences:  A338374 A338375 A338376 * A338378 A338379 A338380

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Oct 23 2020

STATUS

approved

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Last modified October 27 12:59 EDT 2021. Contains 348276 sequences. (Running on oeis4.)