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A049325 A convolution triangle of numbers generalizing Pascal's triangle A007318. 3
1, 6, 1, 16, 12, 1, 16, 68, 18, 1, 0, 224, 156, 24, 1, 0, 448, 840, 280, 30, 1, 0, 512, 3072, 2080, 440, 36, 1, 0, 256, 7872, 10896, 4160, 636, 42, 1, 0, 0, 14080, 42240, 28240, 7296, 868, 48, 1, 0, 0, 16896, 123904, 145376, 60720, 11704, 1136, 54, 1, 0, 0, 12288 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..58.

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*p(3, x))^m, p(3, x) := 1+6*x+16*x^2+16*x^3 (row polynomial of A033842(3, m)).

EXAMPLE

{1}; {6,1}; {16,12,1}; {16,68,18,1}; {0,224,156,24,1}; ...

CROSSREFS

a(n, m) := s1(-3, n, m), a member of a sequence of triangles including s1(0, n, m)= A023531(n, m) (unit matrix) and s1(2, n, m)=A007318(n-1, m-1) (Pascal's triangle). s1(-1, n, m)= A030528, s1(-2, n, m)= A049324(n, m).

Cf. A049349.

Sequence in context: A281288 A278863 A281413 * A250646 A277068 A092371

Adjacent sequences:  A049322 A049323 A049324 * A049326 A049327 A049328

KEYWORD

easy,nonn,tabl

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified November 27 01:16 EST 2021. Contains 349344 sequences. (Running on oeis4.)