A360752 - OEIS

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A360752

Expansion of Sum_{k>0} (x * (1 + (2 * x)^k))^k.

1, 3, 1, 9, 1, 41, 1, 65, 193, 161, 1, 2433, 1, 897, 10241, 18433, 1, 66049, 1, 403457, 344065, 22529, 1, 7127041, 5242881, 106497, 9437185, 73629697, 1, 332890113, 1, 940572673, 230686721, 2228225, 9395240961, 18828754945, 1, 9961473, 5234491393, 429517701121, 1

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..41.

FORMULA

a(n) = Sum_{d|n} 2^(n-d) * binomial(d,n/d-1).

If p is an odd prime, a(p) = 1.

MATHEMATICA

a[n_] := DivisorSum[n, 2^(n-#) * Binomial[#, n/# - 1] &]; Array[a, 40] (* Amiram Eldar, Aug 02 2023 *)

PROG

(PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, (x*(1+(2*x)^k))^k))