A354172 Product_{n>=1} (1 + x^n)^(a(n)/n!) = 1 + sinh(x).

1, 0, 1, -4, 21, -76, 1023, -12160, 65145, -602416, 10925883, -120444160, 1994183205, -21404165056, 372390766023, -12580544512000, 158096182329585, -2119447579092736, 64115697136312563, -1412937791690260480, 27389518837925527965, -616988361649163447296, 19391677044464348893503

Offset

1,4

Links

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

Formula

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

Crossrefs

Cf. A067856, A353608, A353910, A354056, A354171, A354173, A354174, A354175, A354176.

Sequence in context: A240372 A157493 A192429 * A280434 A163697 A134424

Adjacent sequences: A354169 A354170 A354171 * A354173 A354174 A354175

Keyword

sign

Author

Ilya Gutkovskiy, May 18 2022

Status

approved