A026910 a(n) = A026907(2*n, n-1).

28, 154, 627, 2414, 9201, 35094, 134259, 515302, 1983678, 7656374, 29619728, 114822606, 445925707, 1734610302, 6757306947, 26358212502, 102937963242, 402444721782, 1574952822852, 6169131608622, 24184904949252, 94885715007390, 372536351222832, 1463611239163614, 5753766284232606, 22632379126906174, 89072478723401106

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• changed

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000108, A026907.

Programs

Magma

A026910:= func< n | n*Catalan(n) +3*(n+2)*Catalan(n+2) -18 >;
[A026910(n): n in [1..40]]; // G. C. Greubel, Aug 22 2025

Mathematica

Table[n*CatalanNumber[n] +3*(n+2)*CatalanNumber[n+2] -18, {n,40}] (* G. C. Greubel, Aug 22 2025 *)

SageMath

def A026910(n): return binomial(2*n,n-1) +3*binomial(2*n+4,n+1) -18
print([A026910(n) for n in range(1,41)]) # G. C. Greubel, Aug 22 2025

Formula

From G. C. Greubel, Aug 22 2025: (Start)

a(n) = n*A000108(n) + 3*(n+2)*A000108(n+2) - 18.

a(n) = binomial(2*n, n-1) + 3*binomial(2*n+4, n+1) - 18.

G.f.: (3 - 9*x + 7*x^2 - 3*x^3 + 2*x^4 - (3 - 3*x + 7*x^2 + 17*x^3 + 12*x^4)*sqrt(1-4*x))/( 2*(1-x)*x^3*sqrt(1-4*x) ).

E.g.f.: 6 - 18*exp(x) - (1/x^2)*exp(2*x)*( 6*x(1-4*x)*BesselI(0, 2*x) - (6 - 12*x + 25*x^2)*BesselI(1, 2*x) ). (End)

Extensions

More terms added by G. C. Greubel, Aug 22 2025