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A249163 Triangle read by rows: the positive terms of A163626. 3
1, 1, 1, 2, 1, 12, 1, 50, 24, 1, 180, 360, 1, 602, 3360, 720, 1, 1932, 25200, 20160, 1, 6050, 166824, 332640, 40320, 1, 18660, 1020600, 4233600, 1814400, 1, 57002, 5921520, 46070640, 46569600, 3628800, 1, 173052, 33105600, 451725120, 898128000, 239500800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

We have two possibilities: with or without 0's.

Without 0's:

1,

1,

1,   2,

1,  12,

1,  50,  24,

1, 180, 360,

etc.

Sum of every row: A000670(n).

First two terms of successive columns: 1, 1, 2, 12, 24, 360, ... = A211374.

With 0's:

1,   0,    0,   0,

1,   0,    0,   0,

1,   2,    0,   0,

1,  12,    0,   0,

1,  50,   24,   0,

1, 180,  360,   0,

1, 602, 3360, 720,

etc.

The columns are essentially A000012, A028243, A028246, A228909, A228911, A228913, from Stirling numbers of the second kind S(n,3), S(n,5), S(n,7), S(n,9), S(n,11), ... .

LINKS

Table of n, a(n) for n=0..41.

MATHEMATICA

Derivative[0][y][x] = y[x]; Derivative[1][y][x] = y[x]*(1 - y[x]); Derivative[n_][y][x] := Derivative[n][y][x] = D[Derivative[n - 1][y][x], x]; row[n_] := CoefficientList[Derivative[n][y][x], y[x]] // Rest; Table[ Select[row[n], Positive] , {n, 0, 12}] // Flatten

(* or, simply: *) Table[(-1)^k*k!*StirlingS2[n+1, k+1], {n, 0, 12}, {k, 0, n}] // Flatten // Select[#, Positive]& (* Jean-Fran├žois Alcover, Dec 16 2014 *)

CROSSREFS

Cf. A163626, A000670, A211374; also A000012, A000392, A000481, A000771, A049447, A028243, A028246, A091137, A228909, A163626, A228911, A228913 and Worpitzky numbers for the second Bernoulli numbers A164555(n)/A027642(n).

Sequence in context: A118588 A259633 A174500 * A287977 A288367 A288066

Adjacent sequences:  A249160 A249161 A249162 * A249164 A249165 A249166

KEYWORD

nonn,tabf

AUTHOR

Paul Curtz, Dec 15 2014

STATUS

approved

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Last modified July 27 20:33 EDT 2021. Contains 346308 sequences. (Running on oeis4.)