A059822 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)^5 *product_{i=1..t} (1-x^i) ).

0, 1, 6, 20, 55, 119, 246, 435, 766, 1211, 1926, 2807, 4193, 5766, 8161, 10821, 14711, 18820, 24925, 31009, 39984, 48895, 61609, 73844, 91905, 108264, 132400, 154641, 186462, 214772, 257118, 292749, 346430, 392499, 459424, 515579

Offset: 0

Author

N. J. A. Sloane, Feb 24 2001

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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=5