A371066 E.g.f. satisfies A(x) = 1 + x^3/6*exp(x*A(x)).
1, 0, 0, 1, 4, 10, 20, 175, 2296, 20244, 134520, 1016565, 13527580, 209970046, 2785823404, 33569936855, 467250784560, 8358652382760, 159820481883696, 2888819281378089, 51781860691882740, 1031576680142770930, 23237341150372569220, 543570375735294712651
Offset: 0
Keywords
Programs
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Mathematica
nmax = 20; CoefficientList[Series[1 - ProductLog[-E^x*x^4/6]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Mar 10 2024 *) -
PARI
a(n) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n-3*k+1, k)/(6^k*(n-3*k+1)*(n-3*k)!));
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} k^(n-3*k) * binomial(n-3*k+1,k)/( 6^k*(n-3*k+1)*(n-3*k)! ).