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 A360797 Expansion of Sum_{k>0} x^k / (1 - 2 * x^k)^(k+1). 2
 1, 5, 13, 39, 81, 225, 449, 1115, 2345, 5373, 11265, 25483, 53249, 116497, 246405, 529195, 1114113, 2372741, 4980737, 10515511, 22025617, 46204953, 96468993, 201506607, 419432417, 872787997, 1811981789, 3758970975, 7784628225, 16108217801, 33285996545, 68723976779 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..32. FORMULA a(n) = Sum_{d|n} 2^(n/d-1) * binomial(d+n/d-1,d). If p is prime, a(p) = 1 + p * 2^(p-1). MATHEMATICA a[n_] := DivisorSum[n, 2^(n/# - 1) * Binomial[# + n/# - 1, #] &]; Array[a, 30] (* Amiram Eldar, Jul 31 2023 *) PROG (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-2*x^k)^(k+1))) (PARI) a(n) = sumdiv(n, d, 2^(n/d-1)*binomial(d+n/d-1, d)); CROSSREFS Cf. A360798. Sequence in context: A146062 A201612 A129924 * A080143 A077919 A295913 Adjacent sequences: A360794 A360795 A360796 * A360798 A360799 A360800 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 21 2023 STATUS approved

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Last modified October 1 22:38 EDT 2023. Contains 365828 sequences. (Running on oeis4.)