A059821 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)^4 *product_{i=1..t} (1-x^i) ).

0, 1, 5, 14, 34, 64, 121, 190, 311, 446, 666, 887, 1266, 1599, 2169, 2679, 3504, 4178, 5383, 6253, 7858, 9060, 11114, 12560, 15390, 17076, 20512, 22788, 26993, 29494, 34988, 37750, 44213, 47857, 55281, 59196, 68810, 72754, 83518, 88947

Offset

0,3

Links

Table of n, a(n) for n=0..39.

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=4

Crossrefs

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

Sequence in context: A094002 A188589 A105082 * A296010 A182738 A192957

Adjacent sequences: A059818 A059819 A059820 * A059822 A059823 A059824

Keyword

nonn

Author

N. J. A. Sloane, Feb 24 2001

Status

approved