A144496 Row 3 of array in A144502.

7, 37, 229, 1633, 13219, 119917, 1205857, 13318249, 160305343, 2088846709, 29297613277, 440110297777, 7050173910619, 119970793032253, 2161243124917849, 41091937905633337, 822320410135133047, 17277401903869659589, 380267691288777510613, 8749454854573455141889

Offset: 0

Author

David Applegate and N. J. A. Sloane, Dec 13 2008

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A144495, A144497, A144498, A144499, A144500, A144501, A144502, A144503.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( (7-5*x+x^2)*Exp(x)/(1-x)^5 ))); // 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 *)

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

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