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 A237996 Triangular array read by rows.  T(n,k) is the number of even permutations of {1,2,...,n} that have exactly k cycles, n>=0,0<=k<=n. 1
 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 11, 0, 1, 0, 24, 0, 35, 0, 1, 0, 0, 274, 0, 85, 0, 1, 0, 720, 0, 1624, 0, 175, 0, 1, 0, 0, 13068, 0, 6769, 0, 322, 0, 1, 0, 40320, 0, 118124, 0, 22449, 0, 546, 0, 1, 0, 0, 1026576, 0, 723680, 0, 63273, 0, 870, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Row sums = A001710(n). REFERENCES J. Riordan, Introduction to Combinatorial Analysis, Wiley, 1958, page 87, problem # 20. LINKS Alois P. Heinz, Rows n = 0..140, flattened FORMULA E.g.f.: exp(y*A(x))*cosh(y*B(x)) where A(x)= log((1 + x)/(1 - x))^(1/2) and B(x)=log(1/(1-x^2)^(1/2). EXAMPLE 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 11, 0, 1, 0, 24, 0, 35, 0, 1, 0, 0, 274, 0, 85, 0, 1, 0, 720, 0, 1624, 0, 175, 0, 1, 0, 0, 13068, 0, 6769, 0, 322, 0, 1, 0, 40320, 0, 118124, 0, 22449, 0, 546, 0, 1, 0, 0, 1026576, 0, 723680, 0, 63273, 0, 870, 0, 1 MAPLE with(combinat): b:= proc(n, i, t) option remember; expand(`if`(n=0, t, `if`(i<1,       0, add(x^j*multinomial(n, n-i*j, i\$j)*(i-1)!^j/j!*b(n-i*j,       i-1, irem(t+`if`(irem(i, 2)=0, j, 0), 2)), j=0..n/i))))     end: T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(b(n\$2, 1)): seq(T(n), n=0..12);  # Alois P. Heinz, Mar 09 2015 MATHEMATICA nn=11; a=Log[((1+x)/(1-x))^(1/2)]; b=Log[1/(1-x^2)^(1/2)]; Table[Take[(Range[0, nn]!CoefficientList[Series[Exp[y a]Cosh[y b] , {x, 0, nn}], {x, y}])[[n]], n], {n, 1, nn}]//Grid CROSSREFS Sequence in context: A111593 A111594 A322549 * A203951 A323591 A105348 Adjacent sequences:  A237993 A237994 A237995 * A237997 A237998 A237999 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Feb 16 2014 STATUS approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)