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E.g.f.: 1 / (1 + x^2/2 + log(1 - x)).
1

%I #7 Aug 13 2020 22:43:04

%S 1,1,2,8,46,324,2708,26424,295272,3714600,51929472,798610416,

%T 13399081584,243556758912,4767863027328,100004300847744,

%U 2237419620187776,53187370914349440,1338737435337261312,35568441673932566016,994744655047298951424,29211127285363209561600

%N E.g.f.: 1 / (1 + x^2/2 + log(1 - x)).

%F a(0) = 1; a(n) = n * a(n-1) + Sum_{k=3..n} binomial(n,k) * (k-1)! * a(n-k).

%t nmax = 21; CoefficientList[Series[1/(1 + x^2/2 + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!

%t a[0] = 1; a[n_] := a[n] = n a[n - 1] + Sum[Binomial[n, k] (k - 1)! a[n - k], {k, 3, n}]; Table[a[n], {n, 0, 21}]

%Y Cf. A000266, A007840, A226226, A337061.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Aug 13 2020