A049327 A convolution triangle of numbers generalizing Pascal's triangle A007318.

1, 15, 1, 120, 30, 1, 540, 465, 45, 1, 1296, 4680, 1035, 60, 1, 1296, 33192, 15795, 1830, 75, 1, 0, 171072, 176688, 37260, 2850, 90, 1, 0, 641520, 1521828, 563409, 72450, 4095, 105, 1, 0, 1710720, 10359360, 6686064, 1375605, 124740, 5565, 120, 1

Offset

1,2

Links

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

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

Formula

a(n, m) = 6*(6*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(5, x))^m, p(5, x) := 1+15*x+120*x^2+540*x^3+1296*x^4+1296*x^5 (row polynomial of A033842(5, m)).

Example

{1}; {15,1}; {120,30,1}; {540,465,45,1}; {1296,4680,1035,60,1}; ...

Crossrefs

a(n, m) := s1(-5, 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. A049351.

Sequence in context: A040239 A126141 A131514 * A030527 A027467 A049375

Adjacent sequences: A049324 A049325 A049326 * A049328 A049329 A049330

Keyword

easy,nonn,tabl

Author

Wolfdieter Lang

Status

approved