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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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3
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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; refs; listen; history; internal format)
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OFFSET
| 1,5
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REFERENCES
| 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
| There is a simple recurrence.
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EXAMPLE
| 1; 1,1; 1,5,1; 1,14,21,1; 1,30,147,85,1; ...
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MAPLE
| 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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MATHEMATICA
| t[n_, n_] = t[n_, 1] = 1;
t[n_, k_] := t[n-1, k-1] + k^2 t[n-1, k];
Flatten[Table[t[n, k], {n, 1, 10}, {k, n, 1, -1}]][[1 ;; 50]] (* From Jean-François Alcover, Jun 16 2011 *)
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CROSSREFS
| Essentially same as A036969. Cf. A008955.
Sequence in context: A181143 A144438 A157207 * A136267 A109960 A196019
Adjacent sequences: A008954 A008955 A008956 * A008958 A008959 A008960
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KEYWORD
| nonn,nice,easy,tabl
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 16 2000
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