A354274 Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 + arcsinh(x).

1, 0, -1, 4, -11, -4, -547, 7680, -7751, 81744, -3258663, -9474816, -390445563, 233029824, -964154427, 4193551958016, -18431412645519, 71090090006784, -6436900596281679, 17349989459410944, 834261829219880829, -241960391975347200, -1149793471388581053219

Offset

1,4

Links

Table of n, a(n) for n=1..23.

Formula

E.g.f.: Sum_{k>=1} A067856(k) * log(1 + arcsinh(x^k)) / k.

Mathematica

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}]

Crossrefs

Cf. A001818, A067856, A353819, A353914, A353972, A354116, A354172, A354275, A354276.

Sequence in context: A091388 A269742 A151873 * A205136 A096735 A211458

Adjacent sequences: A354271 A354272 A354273 * A354275 A354276 A354277

Keyword

sign

Author

Ilya Gutkovskiy, May 22 2022

Status

approved