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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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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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Adjacent sequences: A000511 A000512 A000513 this_sequence A000515 A000516 A000517
Sequence in context: A052721 A060490 A052722 this_sequence A055360 A001807 A111155
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KEYWORD
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nonn
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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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