A144497 - OEIS

%I #14 Oct 08 2023 04:43:03

%S 37,266,2165,19714,198773,2199722,26516581,345921410,4856217989,

%T 73003575178,1170146049557,19921780455746,359032158501205,

%U 6828661185433514,136693194501702533,2872718327660671042,63240895146440396261,1455362908778264247050,34945987212582211588789

%N Row 4 of array in A144502.

%H Seiichi Manyama, <a href="/A144497/b144497.txt">Table of n, a(n) for n = 0..444</a>

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

%F 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

%t 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)];

%t Table[a[n], {n,0,40}] (* _G. C. Greubel_, Oct 08 2023 *)

%o (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

%o (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

%o (SageMath)

%o def A144497_list(prec):

%o     P.<x> = PowerSeriesRing(QQ, prec)

%o     return P( (37-30*x+9*x^2-x^3)*exp(x)/(1-x)^7 ).egf_to_ogf().list()

%o A144497_list(40) # _G. C. Greubel_, Oct 08 2023

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

%K nonn

%O 0,1

%A _David Applegate_ and _N. J. A. Sloane_, Dec 13 2008