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A269957
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Triangle read by rows, T(n,k) = Sum_{j=k..n} A269940(n,j)*A269939(j,k), for n>=0 and 0<=k<=n.
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0
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1, 0, 1, 0, 5, 9, 0, 41, 210, 225, 0, 469, 5115, 14175, 11025, 0, 6889, 142492, 763350, 1455300, 893025, 0, 123605, 4566149, 41943090, 146522250, 212837625, 108056025, 0, 2620169, 166939742, 2462128095, 13973628900, 35936814375, 42141849750, 18261468225
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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LINKS
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FORMULA
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EXAMPLE
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Triangle starts:
[1]
[0, 1]
[0, 5, 9]
[0, 41, 210, 225]
[0, 469, 5115, 14175, 11025]
[0, 6889, 142492, 763350, 1455300, 893025]
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PROG
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(Sage)
F = lambda n, k, f: sum((-1)^(m+k)*binomial(n+k, n+m)*f(n+m, m) for m in (0..k))
T = lambda n, k: sum(F(n, j, stirling_number1)*F(j, k, stirling_number2) for j in (k..n))
for n in (0..6): print([T(n, k) for k in (0..n)])
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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