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A008957 Triangle of central factorial numbers T(2n,2n-2k), k >= 0, n >= 1 (in Riordan's notation). 5
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; text; internal format)
OFFSET

1,5

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.

LINKS

Reinhard Zumkeller, Rows n = 1..100 of triangle, flattened

F. Alayont and N. Krzywonos, Rook Polynomials in Three and Higher Dimensions, 2012. - From N. J. A. Sloane, Jan 02 2013

FORMULA

There is a simple recurrence.

EXAMPLE

1; 1,1; 1,5,1; 1,14,21,1; 1,30,147,85,1; ...

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

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]] (* Jean-Fran├žois Alcover, Jun 16 2011 *)

PROG

(Haskell)

a008957 n k = a008957_tabl !! (n-1) (k-1)

a008957_row n = a008957_tabl !! (n-1)

a008957_tabl = map reverse a036969_tabl

-- Reinhard Zumkeller, Feb 18 2013

CROSSREFS

Essentially same as A036969. Cf. A008955.

Sequence in context: A181143 A144438 A157207 * A136267 A109960 A196019

Adjacent sequences:  A008954 A008955 A008956 * A008958 A008959 A008960

KEYWORD

nonn,nice,easy,tabl

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Vladeta Jovovic, Apr 16 2000

STATUS

approved

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Last modified February 24 04:33 EST 2018. Contains 299595 sequences. (Running on oeis4.)