OFFSET
0,1
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: (7-5*x+x^2)*exp(x)/(1-x)^5.
a(n) ~ n! * n^4 * exp(1)/8. - Vaclav Kotesovec, Oct 08 2013
a(n) = (n*(n^4 + 10*n^3 + 33*n^2 + 44*n + 21)*a(n-1) + n^2 + 6*n +
7)/(n^4 + 6*n^3 + 9*n^2 + 4*n + 1), with a(0) = 7. - G. C. Greubel, Oct 07 2023
MATHEMATICA
CoefficientList[Series[E^x*(7-5*x+x^2)/(1-x)^5, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 08 2013 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( (7-5*x+x^2)*Exp(x)/(1-x)^5 ))); // G. C. Greubel, Oct 07 2023
(SageMath)
def a(n): # a = A144496
if (n==0): return 7
else: return (n*(n^4+10*n^3+33*n^2+44*n+21)*a(n-1) + n^2+6*n+7)/(n^4+6*n^3+9*n^2+4*n+1)
[a(n) for n in range(41)] # G. C. Greubel, Oct 07 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
David Applegate and N. J. A. Sloane, Dec 13 2008
STATUS
approved