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A202365 G.f.: Sum_{n>=0} (n-x)^n * x^n / (1 + n*x - x^2)^n. 2
1, 1, 2, 10, 54, 336, 2400, 19440, 176400, 1774080, 19595520, 235872000, 3073593600, 43110144000, 647610163200, 10374216652800, 176536039680000, 3180264062976000, 60466862776320000, 1210048630382592000, 25423825985445888000, 559567461880627200000, 12874917427270778880000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

FORMULA

a(n) = (n-1)*(n+2)/2 * (n-1)!, for n>1 with a(0)=a(1)=1.

E.g.f.: 1/2 + 1/(2*(1-x)^2) + x + log(1-x).

E.g.f.: Sum_{n>=0} a(n+1)*x^n/n! = 1/(1-x)^3 - x/(1-x).

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 54*x^4 + 336*x^5 + 2400*x^6 +...

where

A(x) = 1 + (1-x)*x/(1+x-x^2) + (2-x)^2*x^2/(1+2*x-x^2)^2 + (3-x)^3*x^3/(1+3*x-x^2)^3 + (4-x)^4*x^4/(1+4*x-x^2)^4 + (5-x)^5*x^5/(1+5*x-x^2)^5 +...

PROG

(PARI) {a(n)=polcoeff( sum(m=0, n, (m-x)^m*x^m/(1+m*x-x^2 +x*O(x^n))^m), n)}

for(n=0, 30, print1(a(n), ", "))

(PARI) {a(n)=if(n==0|n==1, 1, (n-1)*(n+2)/2 * (n-1)!)}

for(n=0, 30, print1(a(n), ", "))

(PARI) {a(n)=n!*polcoeff(1/2 + 1/(2*(1-x)^2) + x + log(1-x +x*O(x^n)), n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A187742, A187741, A187735, A187746.

Sequence in context: A163909 A272178 A152395 * A330620 A268556 A175935

Adjacent sequences:  A202362 A202363 A202364 * A202366 A202367 A202368

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 09 2013

STATUS

approved

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Last modified June 16 13:56 EDT 2021. Contains 345057 sequences. (Running on oeis4.)