A331617 E.g.f.: exp(1 / (1 - arctan(x)) - 1).

1, 1, 3, 11, 49, 265, 1683, 12035, 95169, 832337, 7998467, 83033403, 922112305, 10978263257, 139956480467, 1889161216179, 26798589518593, 401123509624737, 6346168059440515, 105040097140558699, 1805102151607613361, 32421358229074354601

Offset

0,3

Comments

a(53) is negative. - Vaclav Kotesovec, Jan 26 2020

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A191700(k) * a(n-k).

Mathematica

nmax = 21; CoefficientList[Series[Exp[1/(1 - ArcTan[x]) - 1], {x, 0, nmax}], x] Range[0, nmax]!
A191700[0] = 1; A191700[n_] := A191700[n] = Sum[Binomial[n, k] If[OddQ[k], (-1)^Boole[IntegerQ[(k + 1)/4]] (k - 1)!, 0] A191700[n - k], {k, 1, n}]; a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] A191700[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]

Prog

(PARI) seq(n)={Vec(serlaplace(exp(1/(1 - atan(x + O(x*x^n))) - 1)))} \\ Andrew Howroyd, Jan 22 2020

Crossrefs

Cf. A002019, A110708, A191700, A331610, A331615, A331616, A331618.

Sequence in context: A335788 A012316 A261600 * A193319 A265905 A058733

Adjacent sequences: A331614 A331615 A331616 * A331618 A331619 A331620

Keyword

sign

Author

Ilya Gutkovskiy, Jan 22 2020

Status

approved