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

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn
• tabl

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).

Examples

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

Links

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

Crossrefs

Cf. A039746.

Programs

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}]][[1 ;; 38]]
(* Jean-François Alcover, Jun 21 2011, after g.f. *)

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

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

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