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A049326 A convolution triangle of numbers generalizing Pascal's triangle A007318. 3
1, 10, 1, 50, 20, 1, 125, 200, 30, 1, 125, 1250, 450, 40, 1, 0, 5250, 4375, 800, 50, 1, 0, 15000, 30375, 10500, 1250, 60, 1, 0, 28125, 157500, 100500, 20625, 1800, 70, 1, 0, 31250, 621875, 740000, 250625, 35750, 2450, 80, 1, 0, 15625, 1875000, 4318750 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
FORMULA
a(n, m) = 5*(5*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(4, x))^m, p(4, x) := 1+10*x+50*x^2+125*x^3+125*x^4 (row polynomial of A033842(4, m)).
EXAMPLE
{1}; {10,1}; {50,20,1}; {125,200,30,1}; {125,1250,450,40,1}; ...
CROSSREFS
a(n, m) := s1(-4, 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.
Cf. A049350.
Sequence in context: A115097 A050313 A116574 * A146537 A050304 A143471
KEYWORD
easy,nonn,tabl
AUTHOR
STATUS
approved

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Last modified July 23 04:24 EDT 2024. Contains 374544 sequences. (Running on oeis4.)