The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A271700 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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.
(history; published version)

#7 by Bruno Berselli at Mon Apr 18 06:38:22 EDT 2016

STATUS

reviewed

approved

#6 by Joerg Arndt at Mon Apr 18 06:20:52 EDT 2016

STATUS

proposed

reviewed

#5 by Peter Luschny at Mon Apr 18 04:53:36 EDT 2016

STATUS

editing

proposed

#4 by Peter Luschny at Mon Apr 18 04:36:04 EDT 2016

CROSSREFS

A000027 (col. 1), A000217, A161680 (col. 2), A005581 (col. 3), A211210 (diag. n,n), A211211 (diag. n,n-1).

#3 by Peter Luschny at Mon Apr 18 04:00:24 EDT 2016

MATHEMATICA

Flatten[Table[Sum[(-1)^(n-j)Binomial[-j-1, -n-1] Abs[StirlingS1[k, j]], {j, 0, n}], {n, 0, 9}, {k, 0, n}]]

#2 by Peter Luschny at Thu Apr 14 04:55:45 EDT 2016

NAME

allocated 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 Peter Luschnyn>=0 and 0<=k<=n.

DATA

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

0,5

EXAMPLE

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]

MAPLE

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);

KEYWORD

allocated

nonn,tabl

AUTHOR

Peter Luschny, Apr 14 2016

STATUS

approved

editing

#1 by Peter Luschny at Tue Apr 12 10:16:30 EDT 2016

NAME

allocated for Peter Luschny

KEYWORD

allocated

STATUS

approved