A026911 - OEIS

A026911

a(n) = A026907(2*n, n-2).

67, 348, 1495, 6108, 24501, 97456, 385900, 1524066, 6009720, 23675882, 93226503, 367005692, 1444728537, 5687662392, 22395051912, 88199397642, 347448657492, 1369107075762, 5396498311992, 21277355051610, 83918011194996, 331073286677058, 1306540603377930, 5157617675058838, 20365730134359298, 80440031466243942

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 2..1000

FORMULA

From G. C. Greubel, Aug 23 2025: (Start)

a(n) = binomial(2*n, n-2) + 3*binomial(2*n+4, n) - 18.

G.f.: (3 - 15*x + 19*x^2 - 11*x^3 + 6*x^4 - 2*x^5 - (3 - 9*x + 7*x^2 - 3*x^3 + 8*x^4 + 30*x^5)*sqrt(1-4*x))/(2*(1-x)*x^4*sqrt(1-4*x)).

E.g.f.: 15 - 18*exp(x) + (1/x^3)*exp(2*x)*(6*x*(3 - 4*x + 4*x^2)*BesselI(0, 2*x) - 6*(3 - 4*x + 5*x^2 - 4*x^3)*BesselI(1, 2*x) + x^3*BesselI(2, 2*x) ). (End)

a(n) ~ 49 * 4^n / sqrt(Pi*n). - Amiram Eldar, Oct 28 2025

MATHEMATICA

Table[Binomial[2*n, n-2] +3*Binomial[2*n+4, n] -18, {n, 2, 45}] (* G. C. Greubel, Aug 23 2025 *)

PROG

(Magma)

A026911:= func< n | Binomial(2*n, n-2) +3*Binomial(2*n+4, n) -18 >;

[A026911(n): n in [2..45]]; // G. C. Greubel, Aug 23 2025

(SageMath)

def A026911(n): return binomial(2*n, n-2) +3*binomial(2*n+4, n) -18

print([A026911(n) for n in range(2, 46)]) # G. C. Greubel, Aug 23 2025

CROSSREFS

Cf. A026907.