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 A060523 Triangle T(n,k) = number of degree-n permutations with k even cycles, k=0..n. 4
 1, 1, 0, 1, 1, 0, 3, 3, 0, 0, 9, 12, 3, 0, 0, 45, 60, 15, 0, 0, 0, 225, 345, 135, 15, 0, 0, 0, 1575, 2415, 945, 105, 0, 0, 0, 0, 11025, 18480, 9030, 1680, 105, 0, 0, 0, 0, 99225, 166320, 81270, 15120, 945, 0, 0, 0, 0, 0, 893025, 1596105, 897750, 217350, 23625, 945, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 REFERENCES I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, p. 189, Exercise 3.3.13. LINKS Alois P. Heinz, Rows n = 0..140, flattened FORMULA E.g.f.: (1+x)^((1-y)/2)/(1-x)^((1+y)/2). EXAMPLE Triangle T(n,k) begins: 1; 1, 0; 1, 1, 0; 3, 3, 0, 0; 9, 12, 3, 0, 0; 45, 60, 15, 0, 0, 0; 225, 345, 135, 15, 0, 0, 0; 1575, 2415, 945, 105, 0, 0, 0, 0; 11025, 18480, 9030, 1680, 105, 0, 0, 0, 0; 99225, 166320, 81270, 15120, 945, 0, 0, 0, 0, 0; 893025, 1596105, 897750, 217350, 23625, 945, 0, 0, 0, 0, 0; ... MAPLE with(combinat): b:= proc(n, i) option remember; expand(`if`(n=0, 1, `if`(i<1, 0,       add(multinomial(n, n-i*j, i\$j)*(i-1)!^j/j!*b(n-i*j, i-1)*       `if`(irem(i, 2)=0, x^j, 1), j=0..n/i))))     end: T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(b(n\$2)): seq(T(n), n=0..12);  # Alois P. Heinz, Mar 09 2015 MATHEMATICA nn = 6; Range[0, nn]! CoefficientList[    Series[(1 - x^2)^(-y/2) ((1 + x)/(1 - x))^(1/2), {x, 0, nn}], {x, y}] // Grid  (* Geoffrey Critzer, Aug 27 2012 *) CROSSREFS Cf. A060524. Sequence in context: A299904 A221768 A283071 * A199041 A199237 A309651 Adjacent sequences:  A060520 A060521 A060522 * A060524 A060525 A060526 KEYWORD easy,nonn,tabl AUTHOR Vladeta Jovovic, Apr 01 2001 STATUS approved

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Last modified January 22 01:28 EST 2022. Contains 350481 sequences. (Running on oeis4.)