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Search: id:A000514
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| A000514 |
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Eulerian numbers. (Column 6 of Euler's triangle A008292.)
(Formerly M5379 N2336)
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+0
2
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| 1, 120, 4293, 88234, 1310354, 15724248, 162512286, 1505621508, 12843262863, 102776998928, 782115518299, 5717291972382, 40457344748072, 278794377854832, 1879708669896492, 12446388300682056, 81180715002105741
(list; graph; listen)
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OFFSET
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6,2
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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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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. 260.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 215.
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FORMULA
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6^(n+6-1)+sum(i=1, 6-1, (-1)^i/i!*(6-i)^(n+6-1)*prod(j=1, i, n+6+1-j)) - Randall L. Rathbun (randallr(AT)abac.com), Jan 23 2002
G.f.: (1/120) * (-e^x(x^5+10x^4+20x^3)+e^{2x}(160x^4+640x^3+480x^2)-e^{3x}(1620x^3+3240x^2+1080x)+e^{4x}(3840x^2+3840x+480)-e^{5x}(3000x+1200)+720e^{6x}) - wenjin Woan (wjwoan(AT)hotmail.com), Oct 25 2007
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PROGRAM
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(PARI) A000514(n)=6^(n+6-1)+sum(i=1, 6-1, (-1)^i/i!*(6-i)^(n+6-1)*prod(j=1, i, n+6+1-j))
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CROSSREFS
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Sequence in context: A052722 A139389 A166596 this_sequence A055360 A001807 A111155
Adjacent sequences: A000511 A000512 A000513 this_sequence A000515 A000516 A000517
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), 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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