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

0,2

Links

Table of n, a(n) for n=0..18.

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

Mathematica

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

Crossrefs

Cf. A354977, A048993.

Sequence in context: A251663 A118794 A222879 * A247736 A155928 A001946

Adjacent sequences: A354975 A354976 A354977 * A354979 A354980 A354981

Keyword

nonn

Author

Peter Luschny, Jun 15 2022

Status

approved