A291632 Column 1 of A122832.

0, 1, 2, 9, 28, 125, 486, 2317, 10424, 53433, 267850, 1470161, 8032212, 46925749, 275437358, 1702883925, 10630404976, 69192858737, 455957606034, 3110617216153, 21512638153100, 153234193139181, 1107087138215542, 8206182165264029, 61703155328534568

Offset: 0

Author

Vaclav Kotesovec, Aug 28 2017

Keywords

• nonn

Crossrefs

Cf. A122832, A047974.

Programs

Mathematica

Table[n!*Sum[Binomial[i, n - 1 - i]/i!, {i, 0, n - 1}], {n, 0, 30}]
CoefficientList[Series[x*E^(x*(x+1)), {x, 0, 20}], x] * Range[0, 20]!

Formula

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

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

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