

A055101


Expansion of square of continued fraction 1/ ( 1+q/ ( 1+q^2/ ( 1+q^3/ ( 1+q^4/... )))).


16



1, 2, 3, 2, 1, 4, 6, 6, 3, 2, 9, 16, 17, 10, 5, 24, 36, 36, 21, 10, 46, 74, 77, 42, 22, 94, 144, 142, 78, 38, 172, 266, 266, 146, 73, 312, 471, 464, 251, 122, 534, 814, 801, 432, 213, 910, 1364, 1328, 713, 344, 1485, 2234, 2178
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OFFSET

0,2


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), 918925.


FORMULA

a(0) = 1, a(n) = (2/n)*Sum_{k=1..n} A109091(k)*a(nk) for n > 0.  Seiichi Manyama, Apr 16 2017
Euler transform of period 5 sequence [2, 2, 2, 2, 0, ...].  Georg Fischer, Aug 18 2020


CROSSREFS

See A007325 for first power (which has an alternative g.f.), A055102 for cube, A055103 for 4th power.
Sequence in context: A299765 A104411 A216084 * A319108 A238165 A081316
Adjacent sequences: A055098 A055099 A055100 * A055102 A055103 A055104


KEYWORD

sign,easy


AUTHOR

N. J. A. Sloane, Jun 14 2000


EXTENSIONS

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


STATUS

approved



