A308204
G.f.: x * Product_{k>=1} 1/(1 - k*x^k)^a(k).
Original entry on oeis.org
1, 1, 3, 12, 64, 402, 2972, 24884, 233224, 2413402, 27321706, 335811420, 4453678055, 63403359154, 964550068984, 15618677100569, 268256266076840, 4871672594496080, 93282009271337370, 1878417037286803586, 39686436905680824542, 877842387051165865980
Offset: 1
-
a[n_] := a[n] = SeriesCoefficient[x Product[1/(1 - k x^k)^a[k], {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 22}]
a[n_] := a[n] = Sum[Sum[d^(k/d + 1) a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]/(n - 1); a[1] = 1; Table[a[n], {n, 1, 22}]
A308206
G.f.: x * Product_{k>=1} 1/(1 - a(k)*x^k)^k.
Original entry on oeis.org
1, 1, 3, 12, 63, 396, 2926, 24497, 229757, 2377153, 26917186, 330804783, 4387399275, 62455948949, 950123048257, 15384516283921, 264229711285878, 4798448004296966, 91878671010619078, 1850134691327469413, 39088537892778891963, 864610314507158356377
Offset: 1
-
a[n_] := a[n] = SeriesCoefficient[x Product[1/(1 - a[k] x^k)^k, {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 22}]
a[n_] := a[n] = Sum[Sum[d^2 a[d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]/(n - 1); a[1] = 1; Table[a[n], {n, 1, 22}]
A308207
G.f.: x * Product_{k>=1} (1 + a(k)*x^k)^k.
Original entry on oeis.org
1, 1, 2, 8, 39, 240, 1723, 14165, 130459, 1331530, 14894260, 181259007, 2383643794, 33692516860, 509433237073, 8205927166103, 140299345385359, 2537807239717465, 48423816128109123, 972089365983087479, 20481094574718083726, 451904232651000126082
Offset: 1
-
a[n_] := a[n] = SeriesCoefficient[x Product[(1 + a[k] x^k)^k, {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 22}]
a[n_] := a[n] = -Sum[Sum[d^2 (-a[d])^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]/(n - 1); a[1] = 1; Table[a[n], {n, 1, 22}]
A308231
G.f.: x * Product_{k>=1} (1 + k^k*x^k)^(a(k)/k).
Original entry on oeis.org
1, 1, 2, 20, 1296, 811314, 6309590183, 742323285862918, 1556765505923600080263, 67013651952683308325826069725, 67013652019696961835287511727174009053, 1738161546565554966558255056834401765693850396861
Offset: 1
-
a[n_] := a[n] = SeriesCoefficient[x Product[(1 + k^k x^k)^(a[k]/k), {k, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 12}]
a[n_] := a[n] = Sum[Sum[(-1)^(k/d + 1) d^k a[d], {d, Divisors[k]}] a[n - k], {k, 1, n - 1}]/(n - 1); a[1] = 1; Table[a[n], {n, 1, 12}]
Showing 1-4 of 4 results.