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Search: id:A008957
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| A008957 |
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Triangle of central factorial numbers T(2n,2n-2k), k >= 0, n >= 1 (in Riordan's notation). |
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+0
4
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| 1, 1, 1, 1, 5, 1, 1, 14, 21, 1, 1, 30, 147, 85, 1, 1, 55, 627, 1408, 341, 1, 1, 91, 2002, 11440, 13013, 1365, 1, 1, 140, 5278, 61490, 196053, 118482, 5461, 1, 1, 204, 12138, 251498, 1733303, 3255330, 1071799, 21845, 1, 1, 285, 25194, 846260, 10787231
(list; table; graph; listen)
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OFFSET
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1,5
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REFERENCES
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D. Dumont, Interpretations combinatoires des nombres de Genocchi, Duke Math. J., 41 (1974), 305-318.
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217, Table 6.2(a).
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.8.
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FORMULA
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There is a simple recurrence.
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EXAMPLE
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1; 1,1; 1,5,1; 1,14,21,1; 1,30,147,85,1; ...
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MAPLE
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A036969 := proc(n, k) local j; 2*add(j^(2*n)*(-1)^(k-j)/((k-j)!*(k+j)!), j=1..k); end; # Gives rows of triangle in reversed order
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CROSSREFS
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Essentially same as A036969. Cf. A008955.
Sequence in context: A111910 A144438 A157207 this_sequence A136267 A109960 A056940
Adjacent sequences: A008954 A008955 A008956 this_sequence A008958 A008959 A008960
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KEYWORD
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nonn,nice,easy,tabl
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 16 2000
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