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A331611
E.g.f.: exp(1 / (2 - cosh(x)) - 1) (even powers only).
4
1, 1, 10, 241, 10585, 732826, 73233205, 9955632961, 1764233731270, 394629336427021, 108652463882802505, 36084903957564392206, 14217903951354603567385, 6554505383225768210009041, 3493988190176442653240091010, 2131975894217009666242489287001
OFFSET
0,3
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} binomial(2*n-1,2*k-1) * A094088(k) * a(n-k).
a(n) ~ 2^(2*n + 1/4) * exp(1/(2*sqrt(3)*log(2 + sqrt(3))) - 2/3 + sqrt(8*n/log(2 + sqrt(3)))/3^(1/4) - 2*n) * n^(2*n - 1/4) / (3^(1/8) * log(2 + sqrt(3))^(2*n + 1/4)). - Vaclav Kotesovec, Jan 26 2020
MATHEMATICA
nmax = 15; Table[(CoefficientList[Series[Exp[1/(2 - Cosh[x]) - 1], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
A094088[0] = 1; A094088[n_] := A094088[n] = Sum[Binomial[2 n, 2 k] A094088[n - k], {k, 1, n}]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[2 n - 1, 2 k - 1] A094088[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 15}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 22 2020
STATUS
approved