A059824 Expansion of series related to Liouville's Last Theorem: g.f. Sum_{t>=1} (-1)^(t+1) *x^(t*(t+1)/2) / ( (1-x^t)^7 * Product_{i=1..t} (1-x^i) ).

0, 1, 8, 35, 119, 321, 784, 1672, 3389, 6280, 11285, 18971, 31383, 49162, 76322, 113494, 167785, 239086, 340355, 468636, 646058, 865724, 1161936, 1520105, 1997015, 2559758, 3297599, 4157592, 5266644, 6537922, 8168293, 10003615

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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=7

Crossrefs

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

Sequence in context: A285240 A036598 A229403 * A248882 A292479 A301881

Adjacent sequences: A059821 A059822 A059823 * A059825 A059826 A059827

Keyword

nonn

Author

N. J. A. Sloane, Feb 24 2001

Status

approved