OFFSET
1,3
COMMENTS
T(n,k) = number of ways the sums of all components of two 1..n k-vectors can be equal.
T(n,k) is an odd polynomial in n of order 2*k-1.
Examples:
T(n,1) = n.
T(n,2) = (2/3)*n^3 + (1/3)*n.
T(n,3) = (11/20)*n^5 + (1/4)*n^3 + (1/5)*n.
T(n,4) = (151/315)*n^7 + (2/9)*n^5 + (7/45)*n^3 + (1/7)*n.
Table starts:
1 1 1 1 1 ...
2 6 20 70 252 ...
3 19 141 1107 8953 ...
4 44 580 8092 116304 ...
5 85 1751 38165 856945 ...
...
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..3240
FORMULA
T(n,k) = A273975(2*k, n, (n-1)*k). - Andrey Zabolotskiy, Jan 23 2024
EXAMPLE
For n = 3 and k = 2, (1 + x + x^2)^(2*2) = x^8 + 4*x^7 + 10*x^6 + 16*x^5 + 19*x^4 + 16*x^3 + 10*x^2 + 4*x + 1, whose largest coefficient is T(3,2) = 19.
PROG
(PARI) T(n, k) = polcoef(sum(i=0, n-1, x^i)^(2*k), k*(n-1)); \\ Michel Marcus, Jan 23 2024
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jul 24 2009
STATUS
approved