A356540
Expansion of e.g.f. Product_{k>0} 1/(1 - (3 * x)^k)^(1/3^k).
Original entry on oeis.org
1, 1, 6, 40, 496, 5400, 114400, 1760080, 47671680, 1090230400, 34312096000, 916877068800, 39605683532800, 1211405062067200, 55580939301888000, 2260295506653184000, 115398744818925568000, 4928605977341190144000, 305987190350116667392000
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-(3*x)^k)^(1/3^k))))
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a356539(n) = sumdiv(n, d, d*3^(n-d));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=1, i, a356539(j)*v[i-j+1]/(i-j)!)); v;
A359203
a(n) = Sum_{d|n} (n/d) * 3^(n-d).
Original entry on oeis.org
1, 7, 28, 127, 406, 1756, 5104, 20575, 61237, 230122, 649540, 2579932, 6908734, 26044984, 74578888, 269985151, 731794258, 2799670555, 7360989292, 27392181562, 75948764752, 268482753172, 721764371008, 2742292424188, 7078172334031, 25701091008418, 71173405454680
Offset: 1
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a[n_] := DivisorSum[n, 3^(n-#)*n/# &]; Array[a, 27] (* Amiram Eldar, Aug 23 2023 *)
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a(n) = sumdiv(n, d, n/d*3^(n-d));
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my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(3*x)^k)^2))
A358660
a(n) = Sum_{d|n} d * (n/d)^(n-d).
Original entry on oeis.org
1, 4, 12, 76, 630, 7968, 117656, 2105416, 43048917, 1000781420, 25937424612, 743130116112, 23298085122494, 793742455829456, 29192926758107760, 1152930300766980112, 48661191875666868498, 2185915267189632382650, 104127350297911241532860
Offset: 1
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a[n_] := Total[Map[#*(n/#)^(n - #) &, Divisors[n]]];
Table[a[n],{n,1,100}]
a[n_] := DivisorSum[n, (n/#)^(n-#)*# &]; Array[a, 19] (* Amiram Eldar, Aug 27 2023 *)
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a(n) = sumdiv(n, d, d*(n/d)^(n-d));
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my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(k-1)*x^k/(1-k^(k-1)*x^k)^2))
Showing 1-3 of 3 results.