A288235 Coefficients in the expansion of 1/([r]-[2*r]*x+[3*r]*x^2-...); [ ]=floor, r=sqrt(e).

1, 3, 5, 9, 17, 30, 52, 91, 160, 281, 493, 865, 1518, 2664, 4675, 8204, 14397, 25265, 44337, 77805, 136534, 239592, 420441, 737798, 1294700, 2271961, 3986877, 6996242, 12277127, 21544115, 37805987, 66342603, 116419152, 204294349, 358499270, 629100742

Offset

0,2

Comments

A288236(k) = a(k) if and only if k <= 56.

Conjecture: the sequence is strictly increasing.

Links

Table of n, a(n) for n=0..35.

Formula

G.f.: 1/(Sum_{k>=0} [(k+1)*r]*(-x)^k), where r = sqrt(e) and [ ] = floor.

Mathematica

r = Sqrt[E];
u = 1000; (* # initial terms from given series *)
v = 100;  (* # coefficients in reciprocal series *)
CoefficientList[Series[1/Sum[Floor[r*(k + 1)] (-x)^k, {k, 0, u}], {x, 0, v}], x]

Crossrefs

Cf. A078140 (includes guide to related sequences), A288236.

Sequence in context: A279780 A289260 A279595 * A288236 A288237 A288234

Adjacent sequences: A288232 A288233 A288234 * A288236 A288237 A288238

Keyword

nonn,easy

Author

Clark Kimberling, Jul 11 2017

Status

approved