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A030524
A convolution triangle of numbers obtained from A036068.
3
1, 6, 1, 30, 12, 1, 135, 96, 18, 1, 567, 630, 198, 24, 1, 2268, 3654, 1701, 336, 30, 1, 8748, 19440, 12501, 3564, 510, 36, 1, 32805, 96957, 82296, 31644, 6435, 720, 42, 1, 120285, 459756, 498663, 247536, 66915, 10530, 966, 48, 1, 433026, 2092959
OFFSET
1,2
COMMENTS
a(n,m) := s1p(4; n,m), a member of a sequence of unsigned triangles including s1p(2; n,m)= A007318(n-1,m-1) (Pascal's triangle). Signed version: (-1)^(n-m)*a(n,m) := s1(4; n,m).
LINKS
W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
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, n<m; a(n, 0) := 0; a(1, 1)=1. G.f. for m-th column: (x*(1-3*x+3*x^2)/(1-3*x)^3)^m.
EXAMPLE
{1}; {6,1}; {30,12,1}; {135,96,18,1}; {567,630,198,24,1}; ...
CROSSREFS
Cf. A030523, A043553. a(n, 1)= A036068(n-1). Row sums = A043553(n).
Sequence in context: A120105 A120101 A178726 * A327022 A241171 A051930
KEYWORD
easy,nonn,tabl
STATUS
approved