A049324 A convolution triangle of numbers generalizing Pascal's triangle A007318.

1, 3, 1, 3, 6, 1, 0, 15, 9, 1, 0, 18, 36, 12, 1, 0, 9, 81, 66, 15, 1, 0, 0, 108, 216, 105, 18, 1, 0, 0, 81, 459, 450, 153, 21, 1, 0, 0, 27, 648, 1305, 810, 210, 24, 1, 0, 0, 0, 594, 2673, 2970, 1323, 276, 27, 1, 0, 0, 0, 324, 3915, 7938

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn
• tabl

Examples

			{1}; {3,1}; {3,6,1}; {0,15,9,1}; {0,18,36,12,1}; ...
		

Links

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

Crossrefs

a(n, m) := s1(-2, n, m), a member of a sequence of triangles including s1(0, n, m)= A023531(n, m) (unit matrix) and s1(2, n, m)=A007318(n-1, m-1) (Pascal's triangle). s1(-1, n, m)= A030528.

Cf. A049348, A049404.

Formula

a(n, m) = 3*(3*m-n+1)*a(n-1, m)/n + m*a(n-1, m-1)/n, n >= m >= 1; a(n, m) := 0, nA033842(2, m)).