A370931 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*exp(x^3/6)) ).
1, 1, 4, 30, 340, 5180, 99360, 2300830, 62473600, 1946941920, 68507714800, 2686816932800, 116225776497600, 5497681373384200, 282305750023897600, 15640212734095950000, 929908726447266966400, 59061538103044360083200, 3990922849835432102592000
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*exp(x^3/6)))/x)) -
PARI
a(n) = sum(k=0, n\3, (n-3*k)^k*(2*n-3*k)!/(6^k*k!*(n-3*k)!))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} (n-3*k)^k * (2*n-3*k)!/(6^k * k! * (n-3*k)!).