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

0,1

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

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

Sequence in context: A297329 A347726 A339686 * A025012 A039938 A285846

Adjacent sequences: A144493 A144494 A144495 * A144497 A144498 A144499

Keyword

nonn

Author

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

Status

approved