A055103 Expansion of 4th power of continued fraction 1/ ( 1+q/ ( 1+q^2/ ( 1+q^3/ ( 1+q^4/... )))).

1, -4, 10, -16, 15, 0, -30, 64, -81, 60, 12, -128, 250, -312, 234, 32, -443, 848, -1014, 720, 109, -1312, 2448, -2880, 2033, 280, -3550, 6512, -7513, 5184, 744, -8832, 15980, -18252, 12492, 1712, -20745, 37168, -41942, 28352, 3918, -46288, 82146

Offset: 0

Author

N. J. A. Sloane, Jun 14 2000

Keywords

• sign
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• For the third power see G. E. Andrews, Simplicity and surprise in Ramanujan's "Lost" Notebook, Amer. Math. Monthly, 104 (No. 10, Dec. 1997), 918-925.

Crossrefs

See A007325 for first power (which has an alternative g.f.), A055101 for square, A055102 for cube.

Formula

a(0) = 1, a(n) = -(4/n)*Sum_{k=1..n} A109091(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 16 2017

Extensions

More terms from Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 20 2000