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A204066 G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (n + k*x) / (1 + n*x + k*x^2). 4
1, 1, 4, 16, 82, 502, 3574, 29002, 264166, 2668666, 29612014, 358025986, 4684916902, 65966957722, 994546450174, 15984888286642, 272845934899606, 4929166716321706, 93963635086523374, 1884915966747571906, 39691711412770983622, 875410001054417122042, 20180907494704416823774 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..250

FORMULA

a(n) ~ exp(1/2) * n! * n/2. - Vaclav Kotesovec, Nov 02 2014

EXAMPLE

G.f.: A(x) = 1 + x + 4*x^2 + 16*x^3 + 82*x^4 + 502*x^5 + 3574*x^6 +...

where

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

PROG

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

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

CROSSREFS

Cf. A204064, A187741, A187742, A220181.

Sequence in context: A110378 A076997 A092304 * A022564 A123010 A121146

Adjacent sequences:  A204063 A204064 A204065 * A204067 A204068 A204069

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 09 2013

STATUS

approved

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Last modified September 27 16:20 EDT 2020. Contains 337383 sequences. (Running on oeis4.)