Search: id:A000505
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%I A000505 M5317 N2310
%S A000505 1,57,1191,15619,156190,1310354,9738114,66318474,423281535,2571742175,
%T A000505 15041229521,85383238549,473353301060,2575022097600,13796160184500,
%U A000505 73008517581444,382493246941965,1987497491971605,10258045633638475
%N A000505 Eulerian numbers. (Column 5 of Euler's triangle A008292.)
%D A000505 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000505 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000505 L. Carlitz et al., Permutations and sequences with repetions by number 
               of increases, J. Combin. Theory, 1 (1966), 350-374.
%D A000505 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 243.
%D A000505 F. N. David and D. E. Barton, Combinatorial Chance. Hafner, NY, 1962, 
               p. 151.
%D A000505 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied 
               Tables, Cambridge, 1966, p. 260.
%D A000505 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               215.
%F A000505 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
%F A000505 (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
%o A000505 (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)
%Y A000505 Sequence in context: A008390 A008922 A116181 this_sequence A017773 A017720 
               A009702
%Y A000505 Adjacent sequences: A000502 A000503 A000504 this_sequence A000506 A000507 
               A000508
%K A000505 nonn
%O A000505 5,2
%A A000505 N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. 
               Wilson v (rgwv(AT)rgwv.com)
%E A000505 More terms from Christian G. Bower (bowerc(AT)usa.net), May 12 2000

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