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).
Sum_{k=0..n} k * T(n,k) = A092691(n). - Alois P. Heinz, Aug 17 2023
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
KEYWORD
AUTHOR
Vladeta Jovovic, Apr 01 2001
STATUS
approved