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A256549
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Triangle read by rows, T(n,k) = {n,k}*h(k), where {n,k} are the Stirling set numbers and h(k) = hypergeom([-k+1,-k],[],1), for n>=0 and 0<=k<=n.
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2
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1, 0, 1, 0, 1, 3, 0, 1, 9, 13, 0, 1, 21, 78, 73, 0, 1, 45, 325, 730, 501, 0, 1, 93, 1170, 4745, 7515, 4051, 0, 1, 189, 3913, 25550, 70140, 85071, 37633, 0, 1, 381, 12558, 124173, 526050, 1077566, 1053724, 394353, 0, 1, 765, 39325, 567210, 3482451, 10718946, 17386446, 14196708, 4596553
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OFFSET
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0,6
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LINKS
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FORMULA
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Alternating row sums are the signed Bell numbers (-1)^n*A000110(n).
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EXAMPLE
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Triangle starts:
[1]
[0, 1]
[0, 1, 3]
[0, 1, 9, 13]
[0, 1, 21, 78, 73]
[0, 1, 45, 325, 730, 501]
[0, 1, 93, 1170, 4745, 7515, 4051]
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PROG
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(Sage)
A000262 = lambda n: simplify(hypergeometric([-n+1, -n], [], 1))
for n in range(7): [A256549(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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