OFFSET
0,3
COMMENTS
Sum_{k=0..binomial(n,2)} T(n,k)*exp(2*Pi*I*k/n)) = n!. - Vladeta Jovovic, Dec 05 2008
LINKS
Alois P. Heinz, Rows n = 0..36, flattened
FORMULA
From Paul D. Hanna, Dec 15 2008: (Start)
E.g.f.: A(x,q) = exp(e_q(x,q) - 1) = Sum_{n>=0} Sum_{k=0..n(n-1)/2} T(n,k)*q^k*x^n/(n!*faq(n,q)) where e_q(x,q) = Sum_{n>=0} x^n/faq(n,q) and faq(n,q) = Product_{j=1..n} (q^j-1)/(q-1) with faq(0,q)=1.
EXAMPLE
Triangle T(n,k) begins:
1;
1;
3, 1;
13, 8, 8, 1;
73, 63, 89, 78, 41, 15, 1;
501, 544, 909, 1095, 1200, 842, 680, 315, 129, 24, 1;
...
PROG
(PARI) {T(n, k)=local(e_q=sum(j=0, n, x^j/prod(i=1, j, (q^i-1)/(q-1)))+x*O(x^n)); n!*polcoeff(polcoeff(exp(e_q-1), n, x)*prod(j=1, n, (q^j-1)/(q-1)), k, q)} \\ Paul D. Hanna, Dec 15 2008
CROSSREFS
KEYWORD
nonn,tabf,easy
AUTHOR
Vladeta Jovovic, Dec 05 2008
EXTENSIONS
T(0,0)=1 prepended by Alois P. Heinz, Feb 04 2018
STATUS
approved