A123617 Central terms of triangle A123610: a(n) = A123610(2*n,n).

1, 2, 10, 68, 618, 6352, 71188, 841332, 10352618, 131328068, 1706742160, 22619741212, 304685855700, 4160480013848, 57476485976388, 802048167035968, 11290551106506218, 160168176177137896, 2287724464324213972

Offset

0,2

Comments

Related sequences: A123610(2n+1,n) = A000891(n); A123610(2n+2,n) = A123618(n); A123610(2n+2,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)*sumdiv(2*n, d, if(gcd(n, d)==d, eulerphi(d)*binomial(2*n/d, n/d)^2, 0)))}

Crossrefs

Cf. A123610 (triangle); A000891, A123618.

Sequence in context: A165968 A104098 A056755 * A325054 A139715 A293914

Adjacent sequences: A123614 A123615 A123616 * A123618 A123619 A123620

Keyword

nonn

Author

Paul D. Hanna, Oct 03 2006

Status

approved