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

Author

Wolfdieter Lang

Keywords

• easy
• nice
• nonn
• tabl

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).

Examples

			Triangle begins:
      1,
      6,     1;
     42,    12,    1;
    315,   120,   18,   1;
   2457,  1134,  234,  24,  1;
  19656, 10458, 2673, 384, 30, 1;
  ...
		

Links

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

Crossrefs

Cf. A034171, A007318, A035324.

Row sums: A049028(n), n >= 1.

Programs

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 *)

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

G.f. for column m: ((-1+(1-9*x)^(-1/3))/3)^m.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.