A308205
G.f.: x * Product_{k>=1} (1 + k*x^k)^a(k).
Original entry on oeis.org
1, 1, 2, 8, 38, 234, 1679, 13802, 127155, 1297619, 14516296, 176640311, 2322876382, 32831464503, 496399943530, 7995690518504, 136701790293581, 2472679442088700, 47180405307783443, 947116124382018095, 19954735355719570880, 440286840550877179031
Offset: 1
-
a[n_] := a[n] = SeriesCoefficient[x Product[(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}]
A308228
G.f.: x * Product_{k>=1} 1/(1 - k^k*x^k)^(a(k)/k).
Original entry on oeis.org
1, 1, 3, 30, 1956, 1224510, 9523018859, 1120383171258352, 2349614928773045360884, 101143220645945325750097689653, 101143220747088551095300901321325558554, 2623394662131051405254078144558922468191548124266
Offset: 1
-
a[n_] := a[n] = SeriesCoefficient[x Product[1/(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[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.