OFFSET
0,7
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1274
FORMULA
T(n,k) = T(n,n-k).
EXAMPLE
Triangle begins
1;
1, 1;
1, 1, 1;
2, 3, 3, 2;
6, 11, 16, 11, 6;
21, 58, 98, 98, 58, 21;
112, 407, 879, 1087, 879, 407, 112;
853, 4306, 11260, 17578, 17578, 11260, 4306, 853;
11117, 72489, 230505, 436371, 537272, 436371, 230505, 72489, 11117;
PROG
(PARI)
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
edges(v) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]\2)}
S(n, y)={my(s=0); forpart(p=n, s+=permcount(p)*2^edges(p)*prod(i=1, #p, 1+y^p[i])); s/n!}
InvEulerMT(u)={my(n=#u, p=log(1+x*Ser(u)), vars=variables(p)); Vec(sum(i=1, n, moebius(i)*substvec(p + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i) )}
{my(A=InvEulerMT(vector(10, n, S(n, y)))); for(n=0, #A, for(k=0, n, print1(polcoeff(if(n, A[n], 1), k), ", ")); print)} \\ Andrew Howroyd, May 13 2018
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. J. Mathar, May 10 2018
STATUS
approved