A211210
a(n) = Sum_{k=0..n} binomial(n, k)*|S1(n, k)|.
Original entry on oeis.org
1, 1, 3, 16, 115, 1021, 10696, 128472, 1734447, 25937683, 424852351, 7554471156, 144767131444, 2971727661124, 65013102375404, 1509186299410896, 37032678328740751, 957376811266995031, 25999194631060525009, 739741591417352081464, 22000132609456951524051
Offset: 0
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Table[Sum[Binomial[n, k] Abs[StirlingS1[n, k]], {k, 0, n}], {n, 0, 20}]
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a(n) = sum(k=0, n, binomial(n, k)*abs(stirling(n, k, 1))); \\ Michel Marcus, May 10 2021
A317274
a(n) = Sum_{k=0..n} binomial(n,k)*Stirling1(n,k).
Original entry on oeis.org
1, 1, -1, -2, 19, -79, 76, 2640, -36945, 329371, -1861949, -4438774, 355714228, -7292531180, 109844527612, -1277006731104, 8181112825231, 124379387459175, -6806984421310187, 191750786928500050, -4289244423048443149, 80163499107525756105, -1146313133241947091420, 5494990440819210736560
Offset: 0
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Table[Sum[Binomial[n, k] StirlingS1[n, k], {k, 0, n}], {n, 0, 23}]
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a(n) = sum(k=0, n, binomial(n, k)*stirling(n, k, 1)); \\ Michel Marcus, Aug 07 2019
A271700
Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j-1,-n-1)*S1(k,j), S1 the Stirling cycle numbers A132393, for n>=0 and 0<=k<=n.
Original entry on oeis.org
1, 1, 1, 1, 2, 3, 1, 3, 6, 16, 1, 4, 10, 30, 115, 1, 5, 15, 50, 205, 1021, 1, 6, 21, 77, 336, 1750, 10696, 1, 7, 28, 112, 518, 2814, 17766, 128472, 1, 8, 36, 156, 762, 4308, 28050, 207942, 1734447, 1, 9, 45, 210, 1080, 6342, 42528, 322860, 2746815, 25937683
Offset: 0
Triangle starts:
[1]
[1, 1]
[1, 2, 3]
[1, 3, 6, 16]
[1, 4, 10, 30, 115]
[1, 5, 15, 50, 205, 1021]
[1, 6, 21, 77, 336, 1750, 10696]
[1, 7, 28, 112, 518, 2814, 17766, 128472]
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T := (n,k) -> add(abs(Stirling1(k,j))*binomial(-j-1,-n-1)*(-1)^(n-j),j=0..n);
seq(seq(T(n,k), k=0..n), n=0..9);
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Flatten[Table[Sum[(-1)^(n-j)Binomial[-j-1,-n-1] Abs[StirlingS1[k,j]],{j,0,n}], {n,0,9},{k,0,n}]]
Showing 1-3 of 3 results.
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