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Search: id:A001244
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| A001244 |
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Eulerian numbers. (Column 8 of Euler's triangle A008292.)
(Formerly M5457 N2366)
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+0
2
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| 1, 502, 47840, 2203488, 66318474, 1505621508, 27971176092, 447538817472, 6382798925475, 83137223185370, 1006709967915228, 11485644635009424, 124748182104463860, 1300365805079109480, 13093713503185076040
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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L. Carlitz et al., Permutations and sequences with repetions by number of increases, J. Combin. Theory, 1 (1966), 350-374.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 243.
F. N. David and D. E. Barton, Combinatorial Chance. Hafner, NY, 1962, p. 151.
F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 2601.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 215.
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FORMULA
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8^(n+8-1)+sum(i=1, 8-1, (-1)^i/i!*(8-i)^(n+8-1)*prod(j=1, i, n+8+1-j)) - Randall L. Rathbun (randallr(AT)abac.com), Jan 23 2002
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PROGRAM
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(PARI) A001244(n)=8^(n+8-1)+sum(i=1, 8-1, (-1)^i/i!*(8-i)^(n+8-1)*prod(j=1, i, n+8+1-j))
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CROSSREFS
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Adjacent sequences: A001241 A001242 A001243 this_sequence A001245 A001246 A001247
Sequence in context: A093250 A097425 A121577 this_sequence A067949 A133525 A066525
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KEYWORD
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nonn,easy
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AUTHOR
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njas, Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
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More terms from Christian G. Bower (bowerc(AT)usa.net), May 12 2000
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