A132166 - OEIS

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, 567362016, 99302112, 8723925, 424116, 11613, 168, 1

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OFFSET

1,2

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).

LINKS

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

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

Wolfdieter Lang, First ten rows.

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: ((1-(1-6*x)^6)/(36*(1-6*x)^6))^m.

EXAMPLE

Triangle begins:

{1};

{21,1};

{336,42,1};

{4536,1113,63,1};

...

Row polynomial s(3,x)=336*x+42*x^2+x^3.

PROG

(PARI) a(n, m) = if (n<m, 0, if (m==0, 0, if (n==1, 1, 6*(6*m+n-1)*a(n-1, m)/n + m*a(n-1, m-1)/n)));

row(n) = vector(n, m, a(n, m)); \\ Michel Marcus, Sep 29 2025

CROSSREFS

Related triangle A134141 (S1p(7)).

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

Sequence in context: A040461 A260531 A252939 * A092083 A040435 A040434

Adjacent sequences: A132163 A132164 A132165 * A132167 A132168 A132169

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Oct 12 2007

STATUS

approved