A059819 Expansion of series related to Liouville's Last Theorem: g.f. Sum_{t>0} (-1)^(t+1) *x^(t*(t+1)/2) / ( (1-x^t)^2 *Product_{i=1..t} (1-x^i) ).

0, 1, 3, 5, 9, 11, 18, 19, 28, 30, 40, 39, 57, 51, 68, 68, 86, 77, 107, 91, 123, 114, 138, 121, 172, 140, 178, 166, 205, 171, 240, 189, 251, 224, 266, 230, 322, 245, 314, 286, 356, 283, 396, 303, 403, 361, 416, 343, 497, 368, 479, 424, 515, 407

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

G. E. Andrews, Some debts I owe, Séminaire Lotharingien de Combinatoire, Paper B42a, Issue 42, 2000; see (7.4).

Formula

a(n) = (sigma(n)+tau(n)+Sum_{k=0..n} tau(k)*tau(n-k))/2.

G.f.: (F(x)+G(x)^2)/2, where F(x) = Sum_{k>0} (k+1)*x^k/(1-x^k) and G(x) = Sum_{k>0} x^k/(1-x^k). - Vladeta Jovovic, Feb 12 2004

Maple

Mk := proc(k) -1*add( (-1)^n*q^(n*(n+1)/2)/(1-q^n)^k/mul(1-q^i, i=1..n), n=1..101): end; # with k=2

Crossrefs

Cf. A000005 (k=1), here (k=2), A059820 (k=3), ..., A059825 (k=8).

Cf. A000203, A055507.

Sequence in context: A356537 A270836 A100456 * A074986 A307435 A123328

Adjacent sequences: A059816 A059817 A059818 * A059820 A059821 A059822

Keyword

nonn

Author

N. J. A. Sloane, Feb 24 2001

Status

approved