OFFSET
1,4
FORMULA
T(n,k) = Sum_{j=0..n*k} (-1)^j * (n*k-j)! * [z^j] F(k,z)^n, where F(1,z) = 1+z and F(k,z) = ((1-sqrt(1+4*z))/2)^(2*k) + ((1+sqrt(1+4*z))/2)^(2*k) for k >= 2. [Corrected by Pontus von Brömssen, Jun 01 2022]
T(n,k) = A341439(n,n*k). - Pontus von Brömssen, May 31 2022
EXAMPLE
Table T(n,k):
n=1: 0, 0, 1, 2, ...
n=2: 1, 4, 82, 4740, ...
n=3: 2, 80, 43390, 59216648, ...
n=4: 9, 4752, 59216968, 2649391488016, ...
n=5: 44, 440192, 164806652728, 312400218967336992, ...
...
PROG
(PARI) { A277256(n, k) = my(m, s, g); m=n*k; s=sqrt(1+4*x+O(x^(m+1))); g=if(k==1, 1+z, ((1-s)/2)^(2*k)+((1+s)/2)^(2*k))^n; sum(j=0, m, (-1)^j*polcoeff(g, j)*(m-j)!); }
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Max Alekseyev, Oct 07 2016
STATUS
approved