A132166 A convolution triangle of numbers obtained from A036224.

1, 21, 1, 336, 42, 1, 4536, 1113, 63, 1, 54432, 23184, 2331, 84, 1, 598752, 412272, 65205, 3990, 105, 1, 6158592, 6531840, 1518048, 139860, 6090, 126, 1, 60046272, 94618368, 30912840, 4010769, 256410, 8631, 147, 1, 560431872, 1274921856

Offset: 1

Author

Wolfdieter Lang, Oct 12 2007

Keywords

• nonn
• easy
• tabl

Comments

Signed version: (-1)^(n-m)*a(n, m) := s1(7; n,m).

a(n,m) := s1p(7; n,m), a member of a sequence of unsigned triangles including s1p(2; n,m)= A007318(n-1,m-1) (Pascal's triangle), A030523=s1p(3), A036068=s1p(4), A030526=s1p(5) and A030527=s1p(6).

Examples

			{1};{21,1};{336,42,1};{4536,1113,63,1};...; Row polynomial s(3,x)=336*x+42*x^2+x^3.
		

Links

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

Crossrefs

Related triangle A134141 (S1p(7)).

Cf. A036224(n-1), n>=1 (first column). A132167 (row sums). A132168 (alternating row sums).

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

G.f. for m-th column: ((1-(1-6*x)^6)/(36*(1-6*x)^6))^m.

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