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A218680 O.g.f.: A(x) = Sum_{n>=0} n^n*x^n/(1-n*x)^(2*n)/n! * exp(-n*x/(1-n*x)^2). 0
1, 1, 3, 16, 111, 911, 8622, 91414, 1067579, 13564195, 185687381, 2718184470, 42288343176, 695667651368, 12049465530936, 218945489692574, 4160440403683643, 82448824370010887, 1699889286488298603, 36384381642357676480, 806926050321577391347, 18510872795071148287531 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..21.

EXAMPLE

O.g.f.: A(x) = 1 + x + 3*x^2 + 16*x^3 + 111*x^4 + 911*x^5 + 8622*x^6 +...

where

A(x) = 1 + x/(1-x)^2*exp(-x/(1-x)^2) + 2^2*x^2/(1-2*x)^4/2!*exp(-2*x/(1-2*x)^2) + 3^3*x^3/(1-3*x)^6/3!*exp(-3*x/(1-3*x)^2) + 4^4*x^4/(1-4*x)^8/4!*exp(-4*x/(1-4*x)^2) + 5^5*x^5/(1-5*x)^10/5!*exp(-5*x/(1-5*x)^2) +...

simplifies to a power series in x with integer coefficients.

PROG

(PARI) {a(n)=local(A=1+x); A=sum(k=0, n, k^k/(1-k*x)^(2*k)*x^k/k!*exp(-k*x/(1-k*x)^2+x*O(x^n))); polcoeff(A, n)}

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Cf. A134055.

Sequence in context: A286764 A180609 A074540 * A141003 A002404 A097142

Adjacent sequences:  A218677 A218678 A218679 * A218681 A218682 A218683

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 06 2012

STATUS

approved

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Last modified June 16 20:32 EDT 2021. Contains 345069 sequences. (Running on oeis4.)