A346954 - OEIS

%I #8 Aug 09 2021 08:38:47

%S 1,10,65,350,1736,9030,60355,561550,6188996,69919850,781211795,

%T 8854058850,106994019406,1433756147470,21287253921635,339206526695750,

%U 5630710652048216,96341917117951890,1708973354556320875,31787279786739738250,623964823224788294426

%N E.g.f.: -log( 1 - (exp(x) - 1)^4 / 4! ).

%F a(n) = Stirling2(n,4) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * Stirling2(n-k,4) * k * a(k).

%F a(n) ~ (n-1)! / (log(2^(3/4)*3^(1/4) + 1))^n. - _Vaclav Kotesovec_, Aug 09 2021

%t nmax = 24; CoefficientList[Series[-Log[1 - (Exp[x] - 1)^4/4!], {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 4] &

%t a[n_] := a[n] = StirlingS2[n, 4] + (1/n) Sum[Binomial[n, k] StirlingS2[n - k, 4] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 4, 24}]

%Y Cf. A000453, A000629, A003704, A327505, A346390, A346895, A346955.

%K nonn

%O 4,2

%A _Ilya Gutkovskiy_, Aug 08 2021