A353993
Expansion of e.g.f. ( Product_{k>0} 1/(1 - k * x^k) )^(1/(1-x)).
Original entry on oeis.org
1, 1, 8, 63, 668, 7850, 115914, 1847286, 34031024, 682177464, 15049816200, 357564279600, 9212847784392, 252552128708568, 7395084613746816, 229412209982127480, 7524339637608261120, 259675490280634374720, 9418707076419411194304, 357606237255136232451264
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, 1-k*x^k)^(1/(1-x))))
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a353992(n) = n!*sum(k=1, n, sumdiv(k, d, (k/d)^d/d));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, a353992(j)*binomial(i-1, j-1)*v[i-j+1])); v;
A356436
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} d^(k/d) )/k.
Original entry on oeis.org
1, 5, 23, 146, 874, 8124, 62628, 707664, 7860816, 103284000, 1179669600, 24454569600, 324615427200, 5740203974400, 119579523436800, 2688723275212800, 46084905896601600, 1383333631684300800, 26411386476116275200, 868104140064602112000
Offset: 1
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a(n) = n!*sum(k=1, n, sumdiv(k, d, d^(k/d))/k);
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my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, log(1-k*x^k)/k)/(1-x)))
A354340
a(n) = n! * Sum_{k=1..n} ( Sum_{d|k} d^(k/d + 1) )/(k * (n-k)!).
Original entry on oeis.org
1, 7, 38, 264, 1629, 16075, 122366, 1414952, 16076913, 213998983, 2112313774, 53581378400, 664573162941, 9967808211387, 239545427723062, 5933102008956848, 79857813309308609, 2677379355344673255, 44453311791217697686, 1743982053518367438616
Offset: 1
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a(n) = n!*sum(k=1, n, sumdiv(k, d, d^(k/d+1))/(k*(n-k)!));
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my(N=30, x='x+O('x^N)); Vec(serlaplace(-exp(x)*sum(k=1, N, log(1-k*x^k))))
Showing 1-3 of 3 results.
