OFFSET
0,3
COMMENTS
LINKS
Alois P. Heinz, Rows n = 0..250, flattened
FORMULA
E.g.f.: G(t,z) = exp(exp(z)-1+(t-1)z^3/6).
EXAMPLE
T(4,1)=4 because we have 1|234, 134|2, 124|3 and 123|4.
Triangle starts:
1;
1;
2;
4, 1;
11, 4;
32, 20;
113, 80, 10;
422, 385, 70;
...
MAPLE
G:=exp(exp(z)-1+(t-1)*z^3/6): Gser:=simplify(series(G, z=0, 17)): for n from 0 to 14 do P[n]:=sort(n!*coeff(Gser, z, n)) od: for n from 0 to 14 do seq(coeff(P[n], t, k), k=0..floor(n/3)) od; # yields sequence in triangular form
# second Maple program:
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)/j!*
b(n-i*j, i-1)*`if`(i=3, x^j, 1), j=0..n/i))))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n$2)):
seq(T(n), n=0..15); # Alois P. Heinz, Mar 08 2015
MATHEMATICA
nn = 8; k = 3; Range[0, nn]! CoefficientList[
Series[Exp[Exp[x] - 1 + (y - 1) x^k/k!], {x, 0, nn}], {x, y}] // Grid
// Geoffrey Critzer, Aug 26 2012
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Nov 14 2006
STATUS
approved