A354978
a(n) = Sum_{k=0..n} Stirling2(k + n, n), row sums of A354977.
Original entry on oeis.org
1, 2, 11, 122, 2127, 50682, 1528900, 55742458, 2381375519, 116597648906, 6434959707871, 395148541757400, 26718459567126420, 1972367532078679140, 157829428196155580220, 13607551212801836305770, 1257482733143493065605455, 123990702648155791823769270, 12993254659661472801817366105
Offset: 0
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Table[Sum[StirlingS2[k + n, n], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Jun 15 2022 *)
A354797
Triangle read by rows. T(n, k) = |Stirling1(n, k)| * Stirling2(n + k, n) = A132393(n, k) * A048993(n + k, n).
Original entry on oeis.org
1, 0, 1, 0, 3, 7, 0, 12, 75, 90, 0, 60, 715, 2100, 1701, 0, 360, 7000, 36750, 69510, 42525, 0, 2520, 72884, 595350, 1940295, 2692305, 1323652, 0, 20160, 814968, 9549120, 47030445, 109794300, 120023904, 49329280, 0, 181440, 9801000, 156008160, 1076453763, 3723239520, 6733767040, 6065579520, 2141764053
Offset: 0
Table T(n, k) begins:
[0] 1
[1] 0, 1
[2] 0, 3, 7
[3] 0, 12, 75, 90
[4] 0, 60, 715, 2100, 1701
[5] 0, 360, 7000, 36750, 69510, 42525
[6] 0, 2520, 72884, 595350, 1940295, 2692305, 1323652
[7] 0, 20160, 814968, 9549120, 47030445, 109794300, 120023904, 49329280
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T := (n, k) -> abs(Stirling1(n, k))*Stirling2(n + k, n):
for n from 0 to 6 do seq(T(n, k), k = 0..n) od;
Showing 1-2 of 2 results.