A354176 Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 + tanh(x).

1, 0, -2, 8, -24, -16, -720, 12032, 0, -7936, -3628800, -58190848, -479001600, -22368256, 87178291200, 6174957043712, -20922789888000, 47215125069824, -6402373705728000, -164824694455533568, 2432902008176640000, -4951498053124096, -1124000727777607680000

Offset

1,3

Links

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

Formula

E.g.f.: Sum_{k>=1} A067856(k) * log(1 + tanh(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] = 2^(n + 1) (2^(n + 1) - 1) BernoulliB[n + 1]/((n + 1) n!) - b[n, n - 1]; a[n_] := n! c[n]; Table[a[n], {n, 1, 23}]

Crossrefs

Cf. A000182, A067856, A353779, A353912, A354066, A354171, A354172, A354173, A354174, A354175.

Sequence in context: A303861 A138387 A374364 * A007346 A062247 A284951

Adjacent sequences: A354173 A354174 A354175 * A354177 A354178 A354179

Keyword

sign

Author

Ilya Gutkovskiy, May 18 2022

Status

approved