A356406
a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d * (k/d)^d).
Original entry on oeis.org
1, 4, 16, 79, 443, 2968, 22216, 189698, 1792402, 18745036, 213452996, 2653142952, 35448861576, 509724975264, 7824794618208, 128006170541328, 2217950478978576, 40686737647774368, 785852762719168992, 15974195890305405696, 340376906088298319616
Offset: 1
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a(n) = n!*sum(k=1, n, sumdiv(k, d, 1/(d*(k/d)^d)));
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my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-x^k/k))/(1-x)))
A354339
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} 1/(d * (k/d)^d) )/(n-k)!.
Original entry on oeis.org
1, 4, 13, 47, 188, 939, 5332, 36196, 279085, 2464592, 23591753, 259110191, 3030440580, 38874240339, 535736880460, 8027897509136, 126034992483809, 2144006461602308, 38072688073456557, 723023026186433271, 14342481336066795732, 301141522554921194275
Offset: 1
-
a308345(n) = n!*sumdiv(n, d, 1/(d*(n/d)^d));
a(n) = sum(k=1, n, a308345(k)*binomial(n, k));
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my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, log(1-x^k/k))))
A328193
Expansion of e.g.f. Sum_{k>=1} log(1/(1 + (-x)^k/k)).
Original entry on oeis.org
1, 0, 4, 3, 48, 10, 1440, 1890, 85120, 49896, 7257600, 6883800, 958003200, 792277200, 178919989248, 194107914000, 41845579776000, 29714949264000, 12804747411456000, 12900082757417856, 4918792391884800000, 4594737608304480000, 2248001455555215360000
Offset: 1
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a:= n-> n!*add((-1)^(n-d)/(d*(n/d)^d), d=numtheory[divisors](n)):
seq(a(n), n=1..24); # Alois P. Heinz, Oct 30 2019
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nmax = 23; CoefficientList[Series[Sum[Log[1/(1 + (-x)^k/k)], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[n! Sum[(-1)^(n - d)/(d (n/d)^d), {d, Divisors[n]}], {n, 1, 23}]
A356577
Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k) )^x.
Original entry on oeis.org
1, 0, 2, 6, 28, 195, 1248, 11200, 97088, 1036602, 11477230, 142038996, 1883459928, 27044341896, 412487825540, 6745633845210, 116679466051968, 2137078798914128, 41252266236703320, 838320793571448408, 17846205347898263960, 398262850748807921856
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, 1-x^k/k)^x))
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a308345(n) = n!*sumdiv(n, d, 1/(d*(n/d)^d));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=2, i, j*a308345(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;
Showing 1-4 of 4 results.