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A299354
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Regular triangle where T(n,k) is the number of labeled connected k-uniform hypergraphs spanning n vertices.
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4
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1, 0, 1, 0, 4, 1, 0, 38, 11, 1, 0, 728, 958, 26, 1, 0, 26704, 1042632, 32596, 57, 1, 0, 1866256, 34352418950, 34359509614, 2096731, 120, 1, 0, 251548592, 72057319189266922, 1180591620442534312262, 72057594021152435, 268434467, 247, 1, 0, 66296291072
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OFFSET
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1,5
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LINKS
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FORMULA
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Column k is the logarithmic transform of the inverse binomial transform of c(d) = 2^binomial(d,k).
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EXAMPLE
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Triangle begins:
1
0, 1
0, 4, 1
0, 38, 11, 1
0, 728, 958, 26, 1
0, 26704, 1042632, 32596, 57, 1
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MATHEMATICA
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nn=10; Table[SeriesCoefficient[Log[Sum[x^n/n!*Sum[(-1)^(n-d)*Binomial[n, d]*2^Binomial[d, k], {d, 0, n}], {n, 0, nn}]], {x, 0, n}]*n!, {n, nn}, {k, n}]
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CROSSREFS
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Cf. A000005, A001315, A006126, A006129, A038041, A048143, A298422, A299353, A299471, A306020, A306021.
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KEYWORD
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AUTHOR
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STATUS
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approved
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