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Search: id:A059369
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| A059369 |
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Triangle of numbers T(n,k) = T(n-1,k-1) + ((n+k-1)/k)*T(n-1,k), n >= 1, 1<=k<=n, with T(n,1) = n!, T(n,n) = 1; read from right to left. |
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+0
4
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| 1, 1, 2, 1, 4, 6, 1, 6, 16, 24, 1, 8, 30, 72, 120, 1, 10, 48, 152, 372, 720, 1, 12, 70, 272, 828, 2208, 5040, 1, 14, 96, 440, 1576, 4968, 14976, 40320, 1, 16, 126, 664, 2720, 9696, 33192, 115200, 362880, 1, 18, 160, 952, 4380, 17312, 64704, 247968, 996480
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Another version of triangle in A090238 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 14 2007
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 171, #34.
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FORMULA
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G.f. for k-th diagonal: (Sum_{i >= 1} i!*t^i )^k = Sum_{n >= k} T(n, k)*t^n.
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EXAMPLE
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When read from left to right the rows {T(n,k), 1<=k<=n} for n=1,2,3,... are 1; 2,1; 6,4,1; 24,16,6,1; ...
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CROSSREFS
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Cf. A059370, A059371.
Sequence in context: A033884 A062344 A033877 this_sequence A098473 A121757 A109822
Adjacent sequences: A059366 A059367 A059368 this_sequence A059370 A059371 A059372
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KEYWORD
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nonn,tabl,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 28 2001
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Jan 31 2001
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