OFFSET
0,5
LINKS
Paul D. Hanna, Rows n = 0..30, flattened.
EXAMPLE
This triangle begins:
1;
1, 1;
1, 4, 1;
1, 32, 32, 1;
1, 487, 3282, 487, 1;
1, 11113, 657573, 657573, 11113, 1;
1, 335745, 209282906, 1513844855, 209282906, 335745, 1;
1, 12607257, 96673776804, 5580284351032, 5580284351032, 96673776804, 12607257, 1;
1, 565877928, 61162554558200, 31336815578461815, 229089181252258800, 31336815578461815, 61162554558200, 565877928, 1; ...
G.f.: A(x,y) = 1 + (1+y)*x + (1+4*y+y^2)*x^2 + (1+32*y+32*y^2+y^3)*x^3 + (1+487*y+3282*y^2+487*y^3+y^4)*x^4 +...
The logarithm of the g.f. equals the series:
log(A(x,y)) = (1 + y)*x
+ (1 + 6*y + y^2)*x^2/2
+ (1 + 84*y + 84*y^2 + y^3)*x^3/3
+ (1 + 1820*y + 12870*y^2 + 1820*y^3 + y^4)*x^4/4
+ (1 + 53130*y + 3268760*y^2 + 3268760*y^3 + 53130*y^4 + y^5)*x^5/5 +...
in which the coefficients form A209330(n,k) = binomial(n^2, n*k).
PROG
(PARI) {T(n, k)=polcoeff(polcoeff(exp(sum(m=1, n, x^m/m*sum(j=0, m, binomial(m^2, m*j)*y^j))+x*O(x^n)), n, x), k, y)}
for(n=0, 10, for(k=0, n, print1(T(n, k), ", ")); print(""))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Mar 05 2012
STATUS
approved