A194019 E.g.f. = exp(-x*(x+4)/2)/(1-x)^3.

1, 1, 3, 13, 67, 423, 3133, 26479, 251529, 2651041, 30680659, 386635269, 5268724987, 77182895047, 1209369057453, 20180004340087, 357229013263057, 6686021868702081, 131910248042613091, 2735955184504781629, 59512017882001393011, 1354597373468317860391, 32199995769317030466013, 797895597172079337217983

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

D-finite with recurrence a(n) -n*a(n-1) +(-n+1)*a(n-2) -(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Aug 20 2021

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