A249163 Triangle read by rows: the positive terms of A163626.

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

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-François 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