OFFSET
0,14
LINKS
Winston de Greef, Table of n, a(n) for n = 0..11324 (150 antidiagonals)
Eric Weisstein's World of Mathematics, Lambert W-Function.
FORMULA
E.g.f. A_k(x) of column k satisfies A_k(x) = exp(x + k*x^3/6 * A_k(x)^3).
A_k(x) = exp(x - LambertW(-k*x^3/2 * exp(3*x))/3).
A_k(x) = ( -2 * LambertW(-k*x^3/2 * exp(3*x))/(k*x^3) )^(1/3) for k > 0.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, 7, ...
1, 17, 33, 49, 65, 81, 97, ...
1, 161, 321, 481, 641, 801, 961, ...
1, 1351, 2841, 4471, 6241, 8151, 10201, ...
PROG
(PARI) T(n, k) = n! * sum(j=0, n\3, (k/6)^j*(3*j+1)^(n-2*j-1)/(j!*(n-3*j)!));
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Apr 22 2023
STATUS
approved