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A001244 Eulerian numbers. (Column 8 of Euler's triangle A008292.)
(Formerly M5457 N2366)
+0
2
1, 502, 47840, 2203488, 66318474, 1505621508, 27971176092, 447538817472, 6382798925475, 83137223185370, 1006709967915228, 11485644635009424, 124748182104463860, 1300365805079109480, 13093713503185076040 (list; graph; listen)
OFFSET

1,2

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. 2601.

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 215.

FORMULA

8^(n+8-1)+sum(i=1, 8-1, (-1)^i/i!*(8-i)^(n+8-1)*prod(j=1, i, n+8+1-j)) - Randall L. Rathbun (randallr(AT)abac.com), Jan 23 2002

PROGRAM

(PARI) A001244(n)=8^(n+8-1)+sum(i=1, 8-1, (-1)^i/i!*(8-i)^(n+8-1)*prod(j=1, i, n+8+1-j))

CROSSREFS

Sequence in context: A093250 A097425 A121577 this_sequence A160508 A067949 A133525

Adjacent sequences: A001241 A001242 A001243 this_sequence A001245 A001246 A001247

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 November 25 08:46 EST 2009. Contains 167481 sequences.


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