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A001243 Eulerian numbers (Column 7 of Euler's triangle A008292).
(Formerly M5422 N2355)
+0
2
1, 247, 14608, 455192, 9738114, 162512286, 2275172004, 27971176092, 311387598411, 3207483178157, 31055652948388, 285997074307300, 2527925001876036, 21598596303099900, 179385804170146680 (list; graph; listen)
OFFSET

7,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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.

FORMULA

7^(n+7-1)+sum(i=1, 7-1, (-1)^i/i!*(7-i)^(n+7-1)*prod(j=1, i, n+7+1-j)) - Randall L. Rathbun (randallr(AT)abac.com), Jan 23 2002

PROGRAM

(PARI) A001243(n)=7^(n+7-1)+sum(i=1, 7-1, (-1)^i/i!*(7-i)^(n+7-1)*prod(j=1, i, n+7+1-j))

CROSSREFS

Sequence in context: A051153 A166399 A129133 this_sequence A048901 A065146 A064977

Adjacent sequences: A001240 A001241 A001242 this_sequence A001244 A001245 A001246

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)

EXTENSIONS

More terms from Christian G. Bower (bowerc(AT)usa.net), May 12 2000

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Last modified December 4 08:07 EST 2009. Contains 170310 sequences.


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