OFFSET
0,13
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals)
Eric Weisstein's World of Mathematics, Bell Polynomial.
FORMULA
T(n,k) = Sum_{j=0..floor(n/2)} k^j * Stirling2(n,2*j).
T(n,k) = ( Bell_n(sqrt(k)) + Bell_n(-sqrt(k)) )/2, where Bell_n(x) is n-th Bell polynomial.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 0, 0, 0, 0, 0, ...
0, 1, 2, 3, 4, 5, ...
0, 3, 6, 9, 12, 15, ...
0, 8, 18, 30, 44, 60, ...
0, 25, 70, 135, 220, 325, ...
PROG
(PARI) T(n, k) = sum(j=0, n\2, k^j*stirling(n, 2*j, 2));
(PARI) Bell_poly(n, x) = exp(-x)*suminf(k=0, k^n*x^k/k!);
T(n, k) = round((Bell_poly(n, sqrt(k))+Bell_poly(n, -sqrt(k))))/2;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Oct 09 2022
STATUS
approved