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A354174
Product_{n>=1} (1 + x^(2*n))^(a(n)/(2*n)!) = cosh(x).
5
1, 4, -104, 8128, -354944, -21642752, -6204652544, 4286437900288, -47215125069824, -78465506362130432, -51085990673656315904, -35027783166649488637952, -15510963121850795776016384, -7220202338641080038690127872, 7469518701197092988127633473536, 53919400066294168384184259715268608
OFFSET
1,2
FORMULA
E.g.f.: Sum_{k>=1} A067856(k) * log(cosh(x^k)) / k (even powers only).
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 + 1, 2]/n! - b[n, n - 1]; a[n_] := (2 n)! c[2 n]; Table[a[n], {n, 1, 16}]
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, May 18 2022
STATUS
approved