OFFSET
0,7
LINKS
N. J. A. Sloane, Illustration of initial terms of A001372
EXAMPLE
Triangle begins:
1;
0, 1;
1, 1, 1;
2, 3, 1, 1;
6, 7, 4, 1, 1;
13, 19, 9, 4, 1, 1;
40, 47, 27, 10, 4, 1, 1;
100, 130, 68, 29, 10, 4, 1, 1;
291, 343, 195, 76, 30, 10, 4, 1, 1;
797, 951, 523, 220, 78, 30, 10, 4, 1, 1;
2273, 2615, 1477, 600, 228, 79, 30, 10, 4, 1, 1;
MATHEMATICA
Needs["Combinatorica`"]; nn=30; s[n_, k_]:=s[n, k]=a[n+1-k]+If[n<2 k, 0, s[n-k, k]]; a[1]=1; a[n_]:=a[n]=Sum[a[i] s[n-1, i] i, {i, 1, n-1}]/(n-1); rt=Table[a[i], {i, 1, nn}]; cfd=Drop[Apply[Plus, Table[Take[CoefficientList[CycleIndex[CyclicGroup[n], s]/.Table[s[j]->Table[Sum[rt[[i]] x^(k*i), {i, 1, nn}], {k, 1, nn}][[j]], {j, 1, nn}], x], nn], {n, 2, 30}]], 1]; CoefficientList[Series[Product[1/(1-x^i)^cfd[[i]]/(1-y x^i)^rt[[i]], {i, 1, nn-1}], {x, 0, 10}], {x, y}]//Grid (* after code given by Robert A. Russell in A000081 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Oct 14 2012
STATUS
approved