A353972
Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 + arcsin(x).
Original entry on oeis.org
1, 0, 1, -4, 29, -124, 1583, -17088, 124553, -1152816, 20127867, -262838016, 3978820221, -48595514304, 914656587063, -24441484099584, 370244721585681, -5884988565575424, 162968423791332339, -3855257807841017856, 82014901819948738629, -1934570487417807744000, 58311771938510122952559
Offset: 1
-
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[c[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; c[n_] := c[n] = Mod[n, 2] (n - 2)!!/(n (n - 1)!!) - b[n, n - 1]; a[n_] := n! c[n]; Table[a[n], {n, 1, 23}]
A354275
Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 + arctan(x).
Original entry on oeis.org
1, 0, -2, 8, -16, -64, -832, 13824, 8192, -36096, -4228608, -58438656, -398991360, -3452915712, 44581613568, 7144463302656, -17762113880064, 126440605483008, -7331825098948608, -88237584523984896, 3154526750647517184, -27279757707305287680, -1278044473427380666368
Offset: 1
-
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[c[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; c[n_] := c[n] = {1, 0, -1, 0}[[Mod[n, 4, 1]]]/n - b[n, n - 1]; a[n_] := n! c[n]; Table[a[n], {n, 1, 23}]
A354276
Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 + arctanh(x).
Original entry on oeis.org
1, 0, 2, -8, 64, -304, 3968, -43392, 378880, -4002816, 68247552, -995736576, 15949529088, -238273241088, 4760383438848, -113132156780544, 2119956936523776, -42743492966350848, 1123874181449515008, -28901050300546154496, 722523072906903158784, -19401957422023594475520, 589068777481530305937408
Offset: 1
-
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[c[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; c[n_] := c[n] = Mod[n, 2]/n - b[n, n - 1]; a[n_] := n! c[n]; Table[a[n], {n, 1, 23}]
Showing 1-3 of 3 results.