A291632 - OEIS

%I #6 Aug 28 2017 08:59:45

%S 0,1,2,9,28,125,486,2317,10424,53433,267850,1470161,8032212,46925749,

%T 275437358,1702883925,10630404976,69192858737,455957606034,

%U 3110617216153,21512638153100,153234193139181,1107087138215542,8206182165264029,61703155328534568

%N Column 1 of A122832.

%F E.g.f.: x*exp(x*(x+1)).

%F Recurrence: (n-1)*a(n) = n*a(n-1) + 2*(n-1)*n*a(n-2).

%F a(n) ~ 2^(n/2 - 1) * n^((n+1)/2) * exp(sqrt(n/2) - n/2 - 1/8).

%t Table[n!*Sum[Binomial[i, n - 1 - i]/i!, {i, 0, n - 1}], {n, 0, 30}]

%t CoefficientList[Series[x*E^(x*(x+1)), {x, 0, 20}], x] * Range[0, 20]!

%Y Cf. A122832, A047974.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Aug 28 2017