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COMMENTS
| There are 2 versions of Euler's triangle:
* A008292 Classic version of Euler's triangle used by Comtet (1974).
* A173018 Version of Euler's triangle used by Graham, Knuth and Patashnik in Concrete Math. (1990).
Euler's triangle rows and columns indexing conventions:
* A008292 The rows and columns of the Eulerian triangle are both indexed starting from 1. (Classic version: used in the classic books by Riordan and Comtet.)
* A173018 The rows and columns of the Eulerian triangle are both indexed starting from 0.(Graham et al.)
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REFERENCES
| L. Carlitz et al., Permutations and sequences with repetions by number of increases, J. Combin. Theory, 1 (1966), 350-374.
L. Comtet, "Permutations by Number of Rises; Eulerian Numbers." ยง6.5 in Advanced Combinatorics: The Art of Finite and Infinite Expansions, rev. enl. ed. Dordrecht, Netherlands: Reidel, pp. 51 and 240-246, 1974.
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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| 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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