A011793 Triangle of numbers of irreducible Euler sums.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 3, 3, 1, 2, 5, 3, 1, 1, 5, 7, 4, 1, 3, 8, 9, 4, 1, 1, 7, 14, 12, 5, 1, 3, 14, 20, 15, 5, 1, 1, 9, 25, 30, 18, 6, 1, 4, 20, 42, 40, 22, 6, 1, 1, 12, 42, 66, 55, 26, 7, 1

Offset: 1

Author

N. J. A. Sloane, David Broadhurst

Keywords

• nonn
• tabl
• nice

Links

• Vincenzo Librandi, Rows n = 1..100, flattened
• D. J. Broadhurst, On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory, arXiv:hep-th/9604128, 1996.
• R. P. Loh, A. G. Shannon, and A. F. Horadam, Divisibility Criteria and Sequence Generators Associated with Fermat Coefficients, Preprint, 1980. [Taking every other row of this triangle gives the triangle (A258708) in Table 3.]

Crossrefs

Cf. A258708.

Programs

Mathematica

t[n_, k_] := (2/(n+k))*Sum[ If[ EvenQ[d], MoebiusMu[d/2]*Binomial[(n+k)/d, (n-k)/d], 0], {d, Intersection[ Divisors[n+k], Divisors[n-k]]}]; t[1, 1] = t[2, 1] = 1;row[1] = row[2] = {1}; row[n_] := Table[t[n, k], {k, 2 - Mod[n, 2], n-1, 2}]; Flatten[ Table[ row[n], {n, 1, 17}]] (* Jean-François Alcover, Jun 15 2012, after David Broadhurst *)