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A268848
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Number of sequences with 5 copies each of 1,2,...,n and longest increasing subsequence of length n.
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3
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1, 1, 251, 729811, 10258694241, 449363984934526, 47342758641593552281, 10162884447920460534301136, 3969183064899133655031651559801, 2599293828638212400913690945686101111, 2683885055441747960475755652405552969614101
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OFFSET
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0,3
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LINKS
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Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..100 (terms 0..50 from Alois P. Heinz)
J. D. Horton and A. Kurn, Counting sequences with complete increasing subsequences, Congressus Numerantium, 33 (1981), 75-80. MR 681905
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FORMULA
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a(n) ~ sqrt(5) * (3125/24)^n * n^(4*n) / exp(4*n+4). - Vaclav Kotesovec, Feb 21 2016
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MATHEMATICA
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Table[Sum[Sum[Sum[Sum[k!/(i1!*i2!*i3!*i4!*(k - i1 - i2 - i3 - i4)!)*(5*k)!/(i1 + 2*i2 + 3*i3 + 4*i4 + 5*(k - i1 - i2 - i3 - i4))!*(-1)^(i1 + 2*i2 + 3*i3 + 4*i4 + 5*(k - i1 - i2 - i3 - i4) - k)/(24^i1*6^i2*2^ i3), {i4, 0, k - i1 - i2 - i3}], {i3, 0, k - i1 - i2}], {i2, 0, k - i1}], {i1, 0, k}], {k, 0, 15}] (* Vaclav Kotesovec, Mar 02 2016, after Horton and Kurn *)
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CROSSREFS
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Row n=5 of A047909.
Sequence in context: A052239 A089236 A176377 * A177809 A113899 A045182
Adjacent sequences: A268845 A268846 A268847 * A268849 A268850 A268851
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Feb 14 2016
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STATUS
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approved
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