OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..612
FORMULA
a(n) ~ 2^((3*n-1)/2) * exp(-1/32 + sqrt(2*n)/4 - n/2) * n^(n/2). - Vaclav Kotesovec, Oct 15 2017
a(n) = (-2*i)^n * Hermite(n, i/4). - G. C. Greubel, Jul 12 2024
D-finite with recurrence: -8*(n+1)*a(n) - a(n + 1) + a(n + 2) = 0. - Robert Israel, Feb 23 2026
MAPLE
f:= gfun:-rectoproc({-8*(n+1)*a(n) - a(n + 1) + a(n + 2) = 0, a(0)=1, a(1)=1}, a(n), remember);
map(f, [$0..50]); # Robert Israel, Feb 23 2026
MATHEMATICA
CoefficientList[Series[E^(x + 4*x^2), {x, 0, 30}], x] * Range[0, 30]! (* Vaclav Kotesovec, Oct 15 2017 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 15 2017
STATUS
approved