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A194019 E.g.f. = exp(-x*(x+4)/2)/(1-x)^3. 0
1, 1, 3, 13, 67, 423, 3133, 26479, 251529, 2651041, 30680659, 386635269, 5268724987, 77182895047, 1209369057453, 20180004340087, 357229013263057, 6686021868702081, 131910248042613091, 2735955184504781629, 59512017882001393011, 1354597373468317860391, 32199995769317030466013, 797895597172079337217983 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

E.g.f. satisfies (1-x)*f'(x) = (1+x+x^2)*f(x).

LINKS

Table of n, a(n) for n=0..23.

FORMULA

a(n) ~ n!*exp(-5/2)*n^2/2. - Vaclav Kotesovec, Jun 27 2013

MAPLE

read transforms; Order:=25; ics:=f(0)=1;

e1:=(1-x)*diff(f(x), x) = (1+x+x^2)*f(x);

dsolve({e1, ics}, f(x), series);

SERIESTOLISTMULT(rhs(%));

MATHEMATICA

CoefficientList[Series[E^(-x*(x+4)/2)/(1-x)^3, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)

CROSSREFS

Sequence in context: A028418 A180191 A080832 * A020017 A060014 A182666

Adjacent sequences:  A194016 A194017 A194018 * A194020 A194021 A194022

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 12 2011

STATUS

approved

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Last modified April 20 08:45 EDT 2019. Contains 322306 sequences. (Running on oeis4.)