A354978 a(n) = Sum_{k=0..n} Stirling2(k + n, n), row sums of A354977.

1, 2, 11, 122, 2127, 50682, 1528900, 55742458, 2381375519, 116597648906, 6434959707871, 395148541757400, 26718459567126420, 1972367532078679140, 157829428196155580220, 13607551212801836305770, 1257482733143493065605455, 123990702648155791823769270, 12993254659661472801817366105

Offset: 0

Author

Peter Luschny, Jun 15 2022

Keywords

• nonn

Crossrefs

Cf. A354977, A048993.

Programs

Mathematica

Table[Sum[StirlingS2[k + n, n], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Jun 15 2022 *)

Formula

a(n) ~ 2^(2*n) * n^(n-1/2) / (sqrt(2*Pi*(1-c)) * exp(n) * c^n * (2-c)^n), where c = -LambertW(-2*exp(-2)) = -A226775. - Vaclav Kotesovec, Jun 15 2022