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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 (list; table; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..47.

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 * A241171 A051930 A147320

Adjacent sequences:  A030521 A030522 A030523 * A030525 A030526 A030527

KEYWORD

easy,nonn,tabl

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified July 15 14:33 EDT 2019. Contains 325031 sequences. (Running on oeis4.)