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A331610 E.g.f.: exp(1 / (1 - tan(x)) - 1). 3
1, 1, 3, 15, 97, 777, 7379, 80983, 1007137, 13986289, 214383171, 3593224767, 65347120705, 1281151315641, 26928292883795, 603928982033863, 14392387319349697, 363135896514611041, 9669298448057196291, 270932711729869233903, 7967970654277850949025 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

FORMULA

E.g.f.: exp(sin(x) / (cos(x) - sin(x))).

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * 2^(k-1) * A000111(k) * a(n-k).

a(n) ~ 2^(2*n - 1/4) * exp(1/Pi - 1/2 + 2^(3/2)*sqrt(n/Pi) - n) * n^(n - 1/4) / Pi^(n + 1/4). - Vaclav Kotesovec, Jan 27 2020

MATHEMATICA

nmax = 20; CoefficientList[Series[Exp[1/(1 - Tan[x]) - 1], {x, 0, nmax}], x] Range[0, nmax]!

A000111[n_] := If[EvenQ[n], Abs[EulerE[n]], Abs[(2^(n + 1) (2^(n + 1) - 1) BernoulliB[n + 1])/(n + 1)]]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] 2^(k - 1) A000111[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]

CROSSREFS

Cf. A000111, A000828, A003707, A004211, A006229, A331607.

Sequence in context: A143435 A331325 A132437 * A331618 A128081 A186264

Adjacent sequences:  A331607 A331608 A331609 * A331611 A331612 A331613

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 22 2020

STATUS

approved

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Last modified September 26 16:43 EDT 2020. Contains 337374 sequences. (Running on oeis4.)