A123619 a(n) = A123610(2*n+2,n)/(n+1) = A123618(n)/(n+1).

1, 2, 13, 98, 884, 8712, 92033, 1022450, 11819620, 141052808, 1727897780, 21634496072, 275950213712, 3576314656800, 46995009879033, 625082413914450, 8403885788094500, 114069363868845000, 1561609591376307572

Offset

0,2

Comments

Related sequences: A123610(2n,n) = A123617(n); A123610(2n+1,n) = A000891(n); A123610(2n+2,n) = A123618(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+1)^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, A123618.

Sequence in context: A340451 A064325 A365155 * A341954 A187746 A030519

Adjacent sequences: A123616 A123617 A123618 * A123620 A123621 A123622

Keyword

nonn

Author

Paul D. Hanna, Oct 03 2006

Status

approved