Search: id:A000514
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%I A000514 M5379 N2336
%S A000514 1,120,4293,88234,1310354,15724248,162512286,1505621508,12843262863,
%T A000514 102776998928,782115518299,5717291972382,40457344748072,
%U A000514 278794377854832,1879708669896492,12446388300682056,81180715002105741
%N A000514 Eulerian numbers. (Column 6 of Euler's triangle A008292.)
%D A000514 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000514 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000514 L. Carlitz et al., Permutations and sequences with repetions by number 
               of increases, J. Combin. Theory, 1 (1966), 350-374.
%D A000514 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 243.
%D A000514 F. N. David and D. E. Barton, Combinatorial Chance. Hafner, NY, 1962, 
               p. 151.
%D A000514 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied 
               Tables, Cambridge, 1966, p. 260.
%D A000514 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               215.
%F A000514 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
%F A000514 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}(3840\
               x^2+3840x+480)-e^{5x}(3000x+1200)+720e^{6x}) - wenjin Woan (wjwoan(AT)hotmail.com), 
               Oct 25 2007
%o A000514 (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))
%Y A000514 Sequence in context: A052722 A139389 A166596 this_sequence A055360 A001807 
               A111155
%Y A000514 Adjacent sequences: A000511 A000512 A000513 this_sequence A000515 A000516 
               A000517
%K A000514 nonn
%O A000514 6,2
%A A000514 N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. 
               Wilson v (rgwv(AT)rgwv.com)
%E A000514 More terms from Christian G. Bower (bowerc(AT)usa.net), May 12 2000

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