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A293720
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Expansion of e.g.f.: exp(x + 4*x^2).
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10
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1, 1, 9, 25, 241, 1041, 10681, 60649, 658785, 4540321, 51972841, 415198521, 4988808529, 44847866545, 563683953561, 5586645006601, 73228719433921, 788319280278849, 10747425123292105, 124265401483446361, 1757874020223846321, 21640338257575264081
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ 2^((3*n-1)/2) * exp(-1/32 + sqrt(2*n)/4 - n/2) * n^(n/2). - Vaclav Kotesovec, Oct 15 2017
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MATHEMATICA
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CoefficientList[Series[E^(x + 4*x^2), {x, 0, 30}], x] * Range[0, 30]! (* Vaclav Kotesovec, Oct 15 2017 *)
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PROG
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(PARI) my(N=66, x='x+O('x^N)); Vec(serlaplace(exp(x+4*x^2)))
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 30);
Coefficients(R!(Laplace( Exp(x+4*x^2) ))); // G. C. Greubel, Jul 12 2024
(SageMath)
[(-2*i)^n*hermite(n, i/4) for n in range(31)] # G. C. Greubel, Jul 12 2024
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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