A123618 a(n) = A123610(2*n+2,n).

1, 4, 39, 392, 4420, 52272, 644231, 8179600, 106376580, 1410528080, 19006875580, 259613952864, 3587352778256, 50068405195200, 704925148185495, 10001318622631200, 142866058397606500, 2053248549639210000

Offset

0,2

Comments

Related sequences: A123610(2n,n) = A123617(n); A123610(2n+1,n) = A000891(n); A123610(2n+2,n)/(n+1) = A123619(n). a(n) is divisible by (n+1): a(n)/(n+1) = A123619(n).

Links

G. C. Greubel, Table of n, a(n) for n = 0..830

Mathematica

T[_, 0] = 1; T[n_, k_] := 1/n DivisorSum[n, If[GCD[k, #] == #, EulerPhi[#]*Binomial[n/#, k/#]^2, 0] &];
Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* A123610 *)
Table[T[2*n, n], {n, 0, 50}] (* A123617 *)
Table[T[2*n + 2, n], {n, 0, 50}] (* A123618 *)
Table[T[2*n + 2, n]/(n+1), {n, 0, 50}] (* A123619 *)
(* G. C. Greubel, Oct 26 2017 *)

Prog

(PARI) {a(n)=if(n==0, 1, (1/(2*n+2))*sumdiv(2*n+2, d, if(gcd(n, d)==d, eulerphi(d)*binomial((2*n+2)/d, n/d)^2, 0)))}

Crossrefs

Cf. A123610 (triangle); A123617, A000891, A123619.

Sequence in context: A093851 A224755 A241075 * A199757 A046449 A203211

Adjacent sequences: A123615 A123616 A123617 * A123619 A123620 A123621

Keyword

nonn

Author

Paul D. Hanna, Oct 03 2006

Status

approved