A059820 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)^3 *Product_{i=1..t} (1-x^i) ).

0, 1, 4, 9, 19, 30, 52, 70, 107, 136, 191, 226, 314, 352, 463, 523, 664, 717, 919, 964, 1205, 1282, 1546, 1603, 1992, 2009, 2414, 2504, 2958, 2974, 3606, 3553, 4223, 4273, 4936, 4912, 5885, 5685, 6634, 6654, 7664, 7454, 8822, 8454, 9845

Offset

0,3

Links

Table of n, a(n) for n=0..44.

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

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=3

Crossrefs

Cf. A000005 (k=1), A059819 (k=2), A059820 (k=3), ..., A059825 (k=8).

Sequence in context: A199972 A327753 A100448 * A180784 A015618 A086733

Adjacent sequences: A059817 A059818 A059819 * A059821 A059822 A059823

Keyword

nonn

Author

N. J. A. Sloane, Feb 24 2001

Status

approved