A337003 a(n) = Sum_{k=1..n, gcd(n,k) = 1} binomial(n,k)^2.

1, 4, 18, 32, 250, 72, 3430, 6400, 34506, 29000, 705430, 1254816, 10400598, 8281392, 86567400, 300533760, 2333606218, 2172355848, 35345263798, 68442424000, 332533406646, 554415527952, 8233430727598, 12704658876288, 105035376968750

Offset

1,2

Comments

a(n) is a multiple of n^2 for all n.

Links

Table of n, a(n) for n=1..25.

Formula

a(p) = binomial(2*p,p) - 2, where p is prime.

Mathematica

a[n_] := Sum[If[GCD[n, k] == 1, Binomial[n, k]^2, 0], {k, 1, n}]; Table[a[n], {n, 1, 25}]

Prog

(PARI) a(n) = sum(k=1, n, if (gcd(n, k) == 1, binomial(n, k)^2)); \\ Michel Marcus, Aug 12 2020

Crossrefs

Cf. A000984, A056188.

Sequence in context: A363640 A053191 A003474 * A095823 A092116 A083969

Adjacent sequences: A337000 A337001 A337002 * A337004 A337005 A337006

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 10 2020

Status

approved