OFFSET
1,5
LINKS
Alois P. Heinz, Rows n = 1..141, flattened
D. J. Broadhurst and D. Kreimer, Towards cohomology of renormalization...
EXAMPLE
Triangle begins
1;
1, 1;
1, 2, 1;
2, 3, 3, 1;
3, 6, 6, 4, 1;
MAPLE
with(numtheory): A81:= proc(n) option remember; `if`(n<2, n, (add(add(d*A81(d), d=divisors(j)) *A81(n-j), j=1..n-1))/ (n-1)) end: b:= proc(n) option remember; -`if`(n<0, 1, add(b(n-i) *A81(i+1), i=1..n+1)) end: B:= proc(n) add(b(i) *x^i, i=0..n) end: T:= (n, k)-> coeff(B(n)^k, x, n-k): seq(seq(T(n, k), k=1..n), n=1..13); # Alois P. Heinz, Oct 23 2009
MATHEMATICA
A81[n_] := A81[n] = If[n < 2, n, Sum[ Sum[ d*A81[d], {d, Divisors[j]} ] * A81[n-j], {j, 1, n-1}]/(n-1)]; b[n_] := b[n] = -If[n < 0, 1, Sum[ b[n-i]*A81[i+1], {i, 1, n+1}]]; B[n_] := Sum[ b[i]*x^i, {i, 0, n}]; T[n_, k_] := Coefficient[ B[n]^k, x, n-k]; Flatten[ Table[ T[n, k], {n, 1, 12}, {k, 1, n}]] (* Jean-François Alcover, Jan 20 2012, translated from Alois P. Heinz's Maple program *)
CROSSREFS
KEYWORD
AUTHOR
David Broadhurst, Feb 05 2000
EXTENSIONS
More terms from Alois P. Heinz, Oct 23 2009
STATUS
approved