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A144497
Row 4 of array in A144502.
5
37, 266, 2165, 19714, 198773, 2199722, 26516581, 345921410, 4856217989, 73003575178, 1170146049557, 19921780455746, 359032158501205, 6828661185433514, 136693194501702533, 2872718327660671042, 63240895146440396261, 1455362908778264247050, 34945987212582211588789
OFFSET
0,1
LINKS
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
KEYWORD
nonn
AUTHOR
STATUS
approved