OFFSET
0,13
LINKS
Eric Weisstein's World of Mathematics, Pochhammer Symbol.
FORMULA
T(n,k) = Sum_{j=0..floor(n/2)} k^j * |Stirling1(n,2*j)|.
T(n,k) = ( (sqrt(k))_n + (-sqrt(k))_n )/2, where (x)_n is the Pochhammer symbol.
T(0,k) = 1, T(1,k) = 0; T(n,k) = (2*n-3) * T(n-1,k) - (n^2-4*n+4-k) * T(n-2,k).
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, 12, 26, 42, 60, 80, ...
0, 60, 140, 240, 360, 500, ...
PROG
(PARI) T(n, k) = sum(j=0, n\2, k^j*abs(stirling(n, 2*j, 1)));
(PARI) T(n, k) = round((prod(j=0, n-1, sqrt(k)+j)+prod(j=0, n-1, -sqrt(k)+j)))/2;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Oct 10 2022
STATUS
approved