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A030526 A convolution triangle of numbers obtained from A036070. 4
1, 10, 1, 80, 20, 1, 560, 260, 30, 1, 3584, 2720, 540, 40, 1, 21504, 24768, 7480, 920, 50, 1, 122880, 204288, 87552, 15840, 1400, 60, 1, 675840, 1562880, 908352, 225936, 28800, 1980, 70, 1, 3604480, 11264000, 8595200, 2813696, 483920, 47360, 2660, 80 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n,m) := s1p(5; 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(5; n,m).

LINKS

Table of n, a(n) for n=1..44.

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

FORMULA

a(n, m) = 4*(4*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*(1-6*x+16*x^2-16*x^3)/(1-4*x)^4)^m.

EXAMPLE

1;

10,1;

80,20,1;

560,260,30,1;

3584,2720,540,40,1;

...

CROSSREFS

a(n, 1)= A036070(n-1). Row sums = A045624(n).

Sequence in context: A009209 A009227 A305996 * A206819 A178865 A164881

Adjacent sequences:  A030523 A030524 A030525 * A030527 A030528 A030529

KEYWORD

easy,nonn,tabl

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified October 15 13:01 EDT 2018. Contains 316236 sequences. (Running on oeis4.)