A035529 A convolution triangle of numbers obtained from A034171.

1, 6, 1, 42, 12, 1, 315, 120, 18, 1, 2457, 1134, 234, 24, 1, 19656, 10458, 2673, 384, 30, 1, 160056, 95256, 28539, 5148, 570, 36, 1, 1320462, 861597, 292572, 62532, 8775, 792, 42, 1, 11003850, 7760610, 2920347, 713664, 119565, 13770, 1050, 48, 1

Offset

1,2

Comments

a(n,1)= A034171(n-1); a(n,m)=: s2(4; n,m), generalizing s2(2; n,m) := A007318(n-1,m-1) (Pascal), s2(3; n,m) := A035324(n,m).

Links

Table of n, a(n) for n=1..45.

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

Formula

a(n+1, m) = 3*(3*n+m)*a(n, m)/(n+1) + m*a(n, m-1)/(n+1), n >= m >= 1; a(n, m) := 0, n<m; a(n, 0) := 0; a(1, 1)=1; G.f. for column m: ((-1+(1-9*x)^(-1/3))/3)^m.

Example

{1}; {6,1}; {42,12,1}; {315,120,18,1 ]; ...

Mathematica

a[n_, m_] /; n - 1 >= m >= 1 := (m*a[n - 1, m - 1])/n + (3*(m + 3*(n - 1))*a[n - 1, m])/n; a[n_, m_] /; n < m = 0; a[n_, 0] = 0; a[n_, n_] = 1; Flatten[Table[a[n, m], {n, 1, 9}, {m, 1, n}]] (* Jean-François Alcover, Jul 10 2012, from formula *)

Crossrefs

Cf. A034171, A007318, A035324. Row sums: A049028(n), n >= 1.

Sequence in context: A293172 A145356 A145357 * A135893 A051338 A062138

Adjacent sequences: A035526 A035527 A035528 * A035530 A035531 A035532

Keyword

easy,nice,nonn,tabl

Author

Wolfdieter Lang

Status

approved