A052560 -id:A052560 - cp's OEIS frontend

A117826 First four terms of the sequence are doubled, then those numbers are tripled and then those numbers are quadrupled, etc.

1, 2, 3, 4, 2, 4, 6, 8, 6, 12, 18, 24, 24, 48, 72, 96, 120, 240, 360, 480, 720, 1440, 2160, 2880, 5040, 10080, 15120, 20160, 40320, 80640, 120960, 161280, 362880, 725760, 1088640, 1451520, 3628800, 7257600, 10886400, 14515200, 39916800, 79833600

Offset: 1

Robert G. Wilson v, Apr 25 2006

nonn

Cf. A000142, A115425.

Table[n!{1, 2, 3, 4}, {n, 11}] // Flatten

a(4n-3) = A000142(n). a(4n-2)=2*A000142(n)=A052849(n), a(4n-1)=3*A000142(n)=A052560(n), a(4n)=4*A000142(n)=2*A052849(n)=A052578(n).

A137339 A triangular sequence from a functional coefficient expansion of a raising factorial type: p(x,t)=1/(1-t)^(m*x);m=3.

Original entry on oeis.org

1, 0, 3, 0, 3, 9, 0, 6, 27, 27, 0, 18, 99, 162, 81, 0, 72, 450, 945, 810, 243, 0, 360, 2466, 6075, 6885, 3645, 729, 0, 2160, 15876, 43848, 59535, 42525, 15309, 2187, 0, 15120, 117612, 354564, 548289, 476280, 234738, 61236, 6561, 0, 120960, 986256, 3189348

Offset: 1

Roger L. Bagula, Apr 20 2008

Row sums are:
{1, 3, 12, 60, 360, 2520, 20160, 181440, 1814400, 19958400, 239500800}
Also the Bell transform of A052560. For the definition of the Bell transform see A264428. - Peter Luschny, Jan 27 2016

			{1},
{0, 3},
{0, 3, 9},
{0, 6, 27, 27},
{0, 18, 99, 162, 81},
{0, 72, 450, 945, 810, 243},
{0, 360, 2466, 6075, 6885, 3645, 729},
{0, 2160, 15876, 43848, 59535, 42525, 15309, 2187},
{0, 15120, 117612, 354564, 548289, 476280, 234738, 61236, 6561},
{0, 120960, 986256, 3189348, 5450004, 5455107, 3306744, 1194102, 236196, 19683},
{0, 1088640, 9239184, 31662900, 58618080, 65445975, 46126017, 20667150, 5708070, 885735, 59049}

Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), pp. 62 - 63

# The function BellMatrix is defined in A264428.
BellMatrix(n -> 3*n!, 8); # Peter Luschny, Jan 27 2016

Clear[p, g, m]; m = 3; p[t_] = 1/(1 - t)^(m*x); Table[ ExpandAll[n!SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], {n, 0, 10}]; a = Table[n!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
(* Second program: *)
BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
B = BellMatrix[3#!&, rows = 12];
Table[B[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 28 2018, after Peter Luschny *)

p(x,t)=1/(1-t)^(m*x)=Sum[s(x,n)*t^n/n!;m=3. out_n,m=n!*Coefficients( s(x,n)).

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A117826 First four terms of the sequence are doubled, then those numbers are tripled and then those numbers are quadrupled, etc.

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A137339 A triangular sequence from a functional coefficient expansion of a raising factorial type: p(x,t)=1/(1-t)^(m*x);m=3.

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