Original entry on oeis.org
1, 0, 3, -8, 25, -99, 721, -5704, 40881, -340325, 3628801, -41245511, 479001601, -6129725315, 87212177053, -1317906346184, 20922789888001, -354320889234597, 6402373705728001, -121882630320799633, 2432928081076384321, -51041048673495232715
Offset: 1
a(6) = 1 - 10 + 30 - 120 = -99.
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A182927 := proc(n) local d;
add(-n! / (d*(-(n/d)!)^d), d = numtheory[divisors](n)) end:
seq(A182927(i), i = 1..22);
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a[n_] := Sum[ -n!/(d*(-(n/d)!)^d), {d, Divisors[n]}]; Table[a[n], {n, 1, 22}] // Flatten (* Jean-François Alcover, Jul 29 2013 *)
A308345
Expansion of e.g.f. Sum_{k>=1} log(1/(1 - x^k/k)).
Original entry on oeis.org
1, 2, 4, 15, 48, 310, 1440, 11970, 85120, 821016, 7257600, 91707000, 958003200, 13440913200, 178919989248, 2809456650000, 41845579776000, 763629026160000, 12804747411456000, 257140635922025856, 4918792391884800000, 106876408948152480000
Offset: 1
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nmax = 22; CoefficientList[Series[Sum[Log[1/(1 - x^k/k)], {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest
Table[n! Sum[1/(d (n/d)^d), {d, Divisors[n]}], {n, 1, 22}]
A356407
a(n) = n! * Sum_{k=1..n} Sum_{d|k} 1/(d * ((k/d)!)^d).
Original entry on oeis.org
1, 4, 15, 70, 375, 2411, 17598, 146490, 1359291, 13978597, 157393368, 1929989029, 25568858978, 364288345409, 5551537358188, 90142504077194, 1553345359200299, 28317316174307405, 544431381017568696, 11010510372888267555, 233653645911730002976
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)))
A354341
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} 1/(d * ((k/d)!)^d) )/(n-k)!.
Original entry on oeis.org
1, 4, 12, 38, 130, 557, 2877, 18314, 136458, 1180457, 11389081, 122833207, 1446973931, 18594740348, 257507754524, 3835059283282, 60937544854850, 1030871972064485, 18469079943443229, 349656695460113159, 6969526853682012755, 145958486484692023936
Offset: 1
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a182926(n) = n!*sumdiv(n, d, 1/(d*(n/d)!^d));
a(n) = sum(k=1, n, a182926(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!))))
A356579
Expansion of e.g.f. ( Product_{k>0} 1/(1 - x^k/k!) )^x.
Original entry on oeis.org
1, 0, 2, 6, 24, 170, 990, 8267, 67928, 661698, 6923010, 78997457, 983728812, 13101433501, 187893745130, 2869108871085, 46643882262448, 803224515183482, 14618310020427402, 280340253237270977, 5651276469430635620, 119483759770082806035, 2644015844432596590946
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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a182926(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*a182926(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;
Showing 1-5 of 5 results.
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