A081295 a(n) = (-1)^(n+1)* coefficient of x^n in Sum_{k>=1} x^k/(1+2*x^k).

1, 1, 5, 9, 17, 29, 65, 137, 261, 497, 1025, 2085, 4097, 8129, 16405, 32905, 65537, 130845, 262145, 524793, 1048645, 2096129, 4194305, 8390821, 16777233, 33550337, 67109125, 134225865, 268435457, 536855053, 1073741825, 2147516553, 4294968325, 8589869057

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..3319

Formula

a(p) = 2^(p-1)-1 p prime.

a(n) = (-1)^(n+1) * Sum_{d|n} (-2)^(d-1). - Robert Israel, Jun 04 2018

Maple

f:= n -> (-1)^(n+1)*add((-2)^(d-1), d=numtheory:-divisors(n)):
map(f, [$1..100]); # Robert Israel, Jun 04 2018

Prog

(PARI) a(n)=if(n<1, 0, (-1)^(n+1)*polcoeff(sum(k=1, n, x^k/(1+2*x^k), x*O(x^n)), n))

Crossrefs

Cf. A034729.

Sequence in context: A190806 A294774 A192746 * A180565 A233187 A160426

Adjacent sequences: A081292 A081293 A081294 * A081296 A081297 A081298

Keyword

nonn

Author

Benoit Cloitre, Apr 20 2003

Status

approved