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A360801 Expansion of Sum_{k>0} (x / (1 - 2 * x^k))^k. 0
1, 3, 5, 13, 17, 51, 65, 169, 281, 603, 1025, 2373, 4097, 8655, 16685, 33969, 65537, 134151, 262145, 530269, 1050481, 2108439, 4194305, 8420201, 16778337, 33607707, 67120565, 134338493, 268435457, 537151131, 1073741825, 2148024289, 4295035145, 8591048739 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{d|n} 2^(n/d-1) * binomial(d+n/d-2,d-1).
If p is prime, a(p) = 1 + 2^(p-1).
MATHEMATICA
a[n_] := DivisorSum[n, 2^(n/# - 1) * Binomial[# + n/# - 2, # - 1] &]; Array[a, 30] (* Amiram Eldar, Aug 02 2023 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (x/(1-2*x^k))^k))
(PARI) a(n) = sumdiv(n, d, 2^(n/d-1)*binomial(d+n/d-2, d-1));
CROSSREFS
Sequence in context: A080076 A128339 A147506 * A282960 A275969 A359811
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 21 2023
STATUS
approved

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Last modified March 3 10:51 EST 2024. Contains 370511 sequences. (Running on oeis4.)