A049375 A convolution triangle of numbers obtained from A034687.

1, 15, 1, 275, 30, 1, 5500, 775, 45, 1, 115500, 19250, 1500, 60, 1, 2502500, 471625, 44625, 2450, 75, 1, 55412500, 11495000, 1254000, 85000, 3625, 90, 1, 1246781250, 279675000, 34093125, 2698875, 143750, 5025, 105, 1, 28398906250, 6802812500, 907671875, 81125000, 5093125, 224250, 6650, 120, 1

Offset

1,2

Comments

a(n,1) = A034687(n). a(n,m) =: s2(6; n,m), a member of a sequence of unsigned triangles including s2(2; n,m) = A007318(n-1,m-1) (Pascal's triangle). s2(3; n,m) = A035324(n,m), s2(4; n,m) = A035529(n,m), s2(5; n,m) = A048882(n,m).

Links

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

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

Formula

a(n, m) = 5*(5*(n-1)+m)*a(n-1, m)/n + m*a(n-1, m-1)/n, n >= m >= 1; a(n, m) := 0, n<m; a(n, 0) := 0; a(1, 1)=1.

G.f. for m-th column: ((-1+(1-25*x)^(-1/5))/5)^m.

Example

Triangle begins:
  {1};
  {15,1};
  {275,30,1};
  {5500,775,45,1};
  ...

Mathematica

a[n_, m_] := Coefficient[Series[((-1 + (1 - 25*x)^(-1/5))/5)^m, {x, 0, n}], x^n];
Flatten[Table[a[n, m], {n, 1, 9}, {m, 1, n}]]
(* Jean-François Alcover, Jun 21 2011, after g.f. *)

Crossrefs

Cf. A007318, A034687, A035324, A035529, A039746, A048882.

Sequence in context: A049327 A030527 A027467 * A049224 A223517 A027448

Adjacent sequences: A049372 A049373 A049374 * A049376 A049377 A049378

Keyword

easy,nonn,tabl

Author

Wolfdieter Lang

Status

approved