OFFSET
1,2
COMMENTS
Unoriented version of A339228. Equivalence is up to reversal of all parts combined in series.
EXAMPLE
Triangle begins:
1;
2, 2;
4, 14, 10;
11, 84, 168, 98;
30, 522, 2109, 3004, 1396;
98, 3426, 24397, 63094, 67660, 25652;
328, 23404, 274626, 1142420, 2119985, 1805082, 576010;
...
PROG
(PARI) \\ R(n, k) gives colorings using at most k colors as a vector.
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
B(n, Z)={my(p=Z+O(x^2)); for(n=2, n, p=x*Ser(EulerT(Vec(p^2/(1+p)+Z)))); p}
R(n, k)={my(Z=k*x, q=subst(B((n+1)\2, Z), x, x^2), s=subst(Z, x, x^2)+q^2/(1+q), p=Z+O(x^2), t=p); for(n=1, n\2, t=Z + q*(1 + p); p=Z + x*Ser(EulerT(Vec(t+(s-subst(t, x, x^2))/2))) - t); Vec(p+t-Z+B(n, Z))/2}
M(n)={my(v=vector(n, k, R(n, k)~)); Mat(vector(n, k, sum(i=1, k, (-1)^(k-i)*binomial(k, i)*v[i])))}
{my(T=M(8)); for(n=1, #T~, print(T[n, 1..n]))}
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Nov 30 2020
STATUS
approved