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Search: id:A000505
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| A000505 |
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Eulerian numbers. (Column 5 of Euler's triangle A008292.)
(Formerly M5317 N2310)
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+0
2
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| 1, 57, 1191, 15619, 156190, 1310354, 9738114, 66318474, 423281535, 2571742175, 15041229521, 85383238549, 473353301060, 2575022097600, 13796160184500, 73008517581444, 382493246941965, 1987497491971605, 10258045633638475
(list; graph; listen)
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OFFSET
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5,2
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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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5^(n+4)-(n+5)*4^(n+4)+1/2*(n+4)*(n+5)*3^(n+4)-1/6*(n+3)*(n+4)*(n+5)*2^(n+4)+1/24(n+2)*(n+3)*(n+4)*(n+5) - Randall L. Rathbun (randallr(AT)abac.com), Jan 22 2002
(1/24) e^x(x^4+8x^3+12x^2)-4e^{2x}(2x^3/3+2x^2+x)+3e^{3x}(9x^2/2+6x+1)-8e^{4x}(2x+1)+5e^{5x}. - wenjin woan (wjwoan(AT)hotmail.com), Oct 21 2007
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PROGRAM
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(PARI) A(n)=5^(n+4)-(n+5)*4^(n+4)+1/2*(n+4)*(n+5)*3^(n+4)-1/6*(n+3)*(n+4)*(n+5)*2^(n+4)+1/24(n+2)*(n+3)*(n+4)*(n+5)
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CROSSREFS
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Adjacent sequences: A000502 A000503 A000504 this_sequence A000506 A000507 A000508
Sequence in context: A008390 A008922 A116181 this_sequence A017773 A017720 A009702
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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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