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

1,10

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.]

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 *)

Crossrefs

Cf. A258708.

Sequence in context: A339258 A360326 A322976 * A109649 A228106 A334506

Adjacent sequences: A011790 A011791 A011792 * A011794 A011795 A011796

Keyword

nonn,tabl,nice

Author

N. J. A. Sloane, David Broadhurst

Status

approved