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A081295 a(n) = (-1)^(n+1)* coefficient of x^n in Sum_{k>=1} x^k/(1+2*x^k). 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
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
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Apr 20 2003
STATUS
approved

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Last modified February 26 11:46 EST 2024. Contains 370352 sequences. (Running on oeis4.)