A308397
Expansion of e.g.f. exp(Sum_{k>=1} x^(k^2)*(1 - x^(k^2))/k^2).
Original entry on oeis.org
1, 1, -1, -5, 7, 71, -59, -1511, -9295, -1583, 861751, 4039091, -80670281, -606807785, 7674244397, 78614840641, 1146707474401, 12874145737889, -1054507266321425, -19048413877999253, 238097060642380391, 6646823785301856871, -59731575523361439851, -2231444370433747995415
Offset: 0
-
nmax = 23; CoefficientList[Series[Exp[Sum[x^(k^2) (1 - x^(k^2))/k^2, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Product[(1 + x^k)^(LiouvilleLambda[k]/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
A308396
Expansion of e.g.f. exp(-Sum_{k>=1} x^(k^2)/k^2).
Original entry on oeis.org
1, -1, 1, -1, -5, 29, -89, 209, 841, -50905, 458641, -2423521, 8243731, 158742869, -2450634185, 18519809489, -1402926535919, 21355930009679, -139305034406879, 306503668195775, 40578438892908331, -816475138658703091, 6941097158619626311, -24787202385366731311
Offset: 0
-
nmax = 23; CoefficientList[Series[Exp[-Sum[x^(k^2)/k^2, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Product[(1 - x^k)^(LiouvilleLambda[k]/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
A308398
Expansion of e.g.f. exp(Sum_{k>=1} x^(k^2)*(x^(k^2) - 1)/k^2).
Original entry on oeis.org
1, -1, 3, -7, 19, -51, 61, 167, 6777, -107929, 1650691, -17839911, 157217083, -1229269627, 6185945949, -3251776921, -1151787785999, 10138302541647, 532690324952707, -14122245788830279, 443912721023736291, -7480012715591067331, 115775303074594208893, -1392396864130912381017
Offset: 0
-
nmax = 23; CoefficientList[Series[Exp[Sum[x^(k^2) (x^(k^2) - 1)/k^2, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Product[1/(1 + x^k)^(LiouvilleLambda[k]/k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
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