OFFSET
0,6
REFERENCES
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.5.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1403 (rows 0..25)
FORMULA
E.g.f.: sqrt(Sum_{n>=0} exp(x*(1+q)^n)*x^n/n!).
EXAMPLE
Triangle begins:
1;
1;
1, 1;
1, 3, 3;
1, 6, 15, 16, 3;
1, 10, 45, 110, 140, 60, 10;
...
MATHEMATICA
nn=10; f[x_, y_]:=Sum[Sum[Binomial[n, k](1+y)^(k(n-k)), {k, 0, n}]x^n/n!, {n, 0, nn}]; Map[Select[#, #>0&]&, Range[0, nn]!CoefficientList[Series[Exp[Log[f[x, y]]/2], {x, 0, nn}], {x, y}]]//Grid (* Geoffrey Critzer, Sep 05 2013 *)
PROG
(PARI)
T(n)={[Vecrev(p) | p<-Vec(serlaplace(sqrt(sum(k=0, n, exp(x*(1+y)^k + O(x*x^n))*x^k/k! ))))]}
{ my(A=T(6)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Jan 10 2022
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Vladeta Jovovic, Jun 23 2007
STATUS
approved