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A006700
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T(n,3,1), where T(n,k,s) with 0<=s<n is the number of sequences a_1,...,a_(k*n+s) of integers 0,1,...,n such that the 'bumped' sequence b_1,...,b_(k*n+s) has exactly s n's, where b_i=a_i + j (mod n+1) with minimal j>=0 such that b_0,...,b_i contain at most k elements equal to b_i.
(Formerly M4038)
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2
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1, 5, 393, 131473, 117316993, 219639324573, 745567087151089, 4160071323762705545, 35561839228620292884321, 441709871992325805279854773, 7649447738065395278958097645657
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OFFSET
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0,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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Reference gives recurrences.
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MATHEMATICA
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T[k_, m_] := T[k, m] = If[m <= k, 1, Module[{n = Quotient[m, k]}, Sum[Binomial[m - 1, k i - 1] i T[k, k i - 1]T[k, m - k i], {i, 1, n}] + If[n k == m, 0, (n + 1)T[k, m - 1]]]]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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More terms and better description from Reiner Martin, Feb 07 2002
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STATUS
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approved
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