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) * i) + Bell_n(-sqrt(k) * i) )/2, where Bell_n(x) is n-th Bell polynomial and i is the imaginary unit.
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, -6, -10, -12, -12, -10, ...
0, -5, 10, 45, 100, 175, ...
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)*I)+Bell_poly(n, -sqrt(k)*I)))/2;
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Oct 11 2022
STATUS
approved