A354274
Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 + arcsinh(x).
Original entry on oeis.org
1, 0, -1, 4, -11, -4, -547, 7680, -7751, 81744, -3258663, -9474816, -390445563, 233029824, -964154427, 4193551958016, -18431412645519, 71090090006784, -6436900596281679, 17349989459410944, 834261829219880829, -241960391975347200, -1149793471388581053219
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 - 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.