A144497 Row 4 of array in A144502.

37, 266, 2165, 19714, 198773, 2199722, 26516581, 345921410, 4856217989, 73003575178, 1170146049557, 19921780455746, 359032158501205, 6828661185433514, 136693194501702533, 2872718327660671042, 63240895146440396261, 1455362908778264247050, 34945987212582211588789

Offset

0,1

Links

Seiichi Manyama, Table of n, a(n) for n = 0..444

Formula

E.g.f.: exp(x)*(37-30*x+9*x^2-x^3)/(1-x)^7.

a(n) = (n*(n^6 + 21*n^5 + 172*n^4 + 705*n^3 + 1522*n^2 + 1623*n + 653)*a(n-1) - (n^3 + 12*n^2 + 41*n + 37))/(n^6 + 15*n^5 + 82*n^4 + 207*n^3 + 244*n^2 + 105*n - 1), with a(0) = 37. - G. C. Greubel, Oct 08 2023

Mathematica

a[n_]:= If[n<1, 37, (n*(n^6+21*n^5+172*n^4+705*n^3+1522*n^2+1623*n +653)*a[n-1] -(n^3+12*n^2+41*n+37))/(n^6+15*n^5+82*n^4+207*n^3 +244*n^2+105*n-1)];
Table[a[n], {n, 0, 40}] (* G. C. Greubel, Oct 08 2023 *)

Prog

(PARI) my(x='x+O('x^25)); Vec(serlaplace(exp(x)*(37-30*x+9*x^2-x^3)/(1-x)^7)) \\ Michel Marcus, Apr 06 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( (37-30*x+9*x^2-x^3)*Exp(x)/(1-x)^7 ))); // G. C. Greubel, Oct 08 2023
(SageMath)
def A144497_list(prec):
    P.<x> = PowerSeriesRing(QQ, prec)
    return P( (37-30*x+9*x^2-x^3)*exp(x)/(1-x)^7 ).egf_to_ogf().list()
A144497_list(40) # G. C. Greubel, Oct 08 2023

Crossrefs

Cf. A144495, A144496, A144498, A144499, A144500, A144501, A144502, A144503.

Sequence in context: A366934 A119545 A131278 * A219155 A139996 A219740

Adjacent sequences: A144494 A144495 A144496 * A144498 A144499 A144500

Keyword

nonn

Author

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

Status

approved