A049325 A convolution triangle of numbers generalizing Pascal's triangle A007318.

1, 6, 1, 16, 12, 1, 16, 68, 18, 1, 0, 224, 156, 24, 1, 0, 448, 840, 280, 30, 1, 0, 512, 3072, 2080, 440, 36, 1, 0, 256, 7872, 10896, 4160, 636, 42, 1, 0, 0, 14080, 42240, 28240, 7296, 868, 48, 1, 0, 0, 16896, 123904, 145376, 60720, 11704, 1136, 54, 1, 0, 0, 12288

Offset

1,2

Links

Table of n, a(n) for n=1..58.

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

Formula

a(n, m) = 4*(4*m-n+1)*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: (x*p(3, x))^m, p(3, x) := 1+6*x+16*x^2+16*x^3 (row polynomial of A033842(3, m)).

Example

{1}; {6,1}; {16,12,1}; {16,68,18,1}; {0,224,156,24,1}; ...

Crossrefs

a(n, m) := s1(-3, 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, s1(-2, n, m)= A049324(n, m).

Cf. A049349.

Sequence in context: A281288 A278863 A281413 * A250646 A277068 A369904

Adjacent sequences: A049322 A049323 A049324 * A049326 A049327 A049328

Keyword

easy,nonn,tabl

Author

Wolfdieter Lang

Status

approved