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A354978
a(n) = Sum_{k=0..n} Stirling2(k + n, n), row sums of A354977.
1
1, 2, 11, 122, 2127, 50682, 1528900, 55742458, 2381375519, 116597648906, 6434959707871, 395148541757400, 26718459567126420, 1972367532078679140, 157829428196155580220, 13607551212801836305770, 1257482733143493065605455, 123990702648155791823769270, 12993254659661472801817366105
OFFSET
0,2
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
Sequence in context: A251663 A118794 A222879 * A247736 A155928 A001946
KEYWORD
nonn
AUTHOR
Peter Luschny, Jun 15 2022
STATUS
approved