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A361182
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E.g.f. satisfies A(x) = exp( 3*x*A(x) ) / (1-x).
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5
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1, 4, 41, 735, 19293, 672573, 29342241, 1540097541, 94579646553, 6656561754345, 528414534842949, 46716837535074897, 4552821617337191637, 484953672676323320109, 56056228305888242732841, 6988787950179969557086797, 934866118278080385555647025
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = n! * Sum_{k=0..n} 3^k * (k+1)^(k-1) * binomial(n,k)/k!.
E.g.f.: LambertW( -3*x/(1-x) ) / (-3*x).
a(n) ~ (1 + 3*exp(1))^(n + 3/2) * n^(n-1) / (3^(3/2) * exp(n + 1/2)). - Vaclav Kotesovec, Mar 03 2023
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MATHEMATICA
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nmax = 20; A[_] = 1;
Do[A[x_] = Exp[3*x*A[x]]/(1 - x) + O[x]^(nmax+1) // Normal, {nmax}];
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PROG
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(PARI) a(n) = n!*sum(k=0, n, 3^k*(k+1)^(k-1)*binomial(n, k)/k!);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(lambertw(-3*x/(1-x))/(-3*x)))
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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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