OFFSET
0,14
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (first 51 antidiagonals).
Wikipedia, Cactus graph.
FORMULA
EXAMPLE
Array begins:
===================================================
n\k | 1 2 3 4 5 6 ...
----+----------------------------------------------
0 | 1 1 1 1 1 1 ...
1 | 1 1 1 1 1 1 ...
2 | 1 1 1 1 1 1 ...
3 | 1 3 4 6 7 9 ...
4 | 1 7 19 35 57 85 ...
5 | 1 28 124 349 737 1359 ...
6 | 1 108 931 3766 10601 24112 ...
7 | 1 507 7801 45632 167741 471253 ...
8 | 1 2431 68685 580203 2790873 9678999 ...
9 | 1 12441 630850 7687128 48300850 206780448 ...
...
PROG
(PARI) \\ R(n, k) gives A361236.
u(n, k, r) = {r*binomial(n*(2*k-1) + r, n)/(n*(2*k-1) + r)}
R(n, k) = {if(n==0, 1, u(n, k, 1)/((k-1)*n+1) + sumdiv(gcd(k, n-1), d, if(d>1, eulerphi(d)*u((n-1)/d, k, 2*k/d)/k)))}
T(n, k) = {(R(n, k) + u(n\2, k, if(n%2, k, 1)))/2}
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Mar 06 2023
STATUS
approved