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

Comments

In general, for m>=1, Sum_{k=0..n} Stirling2(n + m*k,n) ~ (m+1)^((m+1)*n) * n^(m*n - 1/2) / (sqrt(2*Pi*(1-w)) * exp(m*n) * (m+1-w)^(m*n) * w^n), where w = -LambertW(-(m+1)*exp(-m-1)). - Vaclav Kotesovec, Jan 22 2026

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, A392734.

Sequence in context: A383281 A118794 A222879 * A247736 A155928 A001946

Adjacent sequences: A354975 A354976 A354977 * A354979 A354980 A354981

Keyword

nonn

Author

Peter Luschny, Jun 15 2022

Status

approved