A337058 - OEIS

%I #7 Aug 13 2020 22:42:52

%S 1,1,2,7,33,191,1323,10711,99151,1032385,11943003,151979213,

%T 2109829857,31730171539,513903517585,8917723105003,165065061436755,

%U 3246274767649637,67598797715175999,1485845872704318265,34378343609138619685,835190283258080561671

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

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

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

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

%Y Cf. A000670, A032032, A097514, A102233, A337059.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Aug 13 2020