A336728 a(0) = 1 and a(n) = (1/n) * Sum_{k=1..n} (-n)^(n-k) * binomial(n,k) * binomial(n,k-1) for n > 0.

1, 1, -1, 1, 9, -174, 2575, -38219, 588833, -9274418, 141253551, -1739881142, -753419447, 1379742127908, -83720072007585, 4059017293956301, -184613801568558975, 8254420480122200214, -369177108304219471457, 16608406418618863804990, -750673988803431836351799

Offset: 0

Author

Seiichi Manyama, Aug 02 2020

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..387

Crossrefs

Main diagonal of A336727.

Cf. A242369, A307885, A336713, A336714.

Programs

Mathematica

a[0] = 1; a[n_] := Sum[(-n)^(n - k) * Binomial[n, k] * Binomial[n , k - 1], {k, 1, n}] / n; Array[a, 21, 0] (* Amiram Eldar, Aug 02 2020 *)

PARI

{a(n) = if(n==0, 1, sum(k=1, n, (-n)^(n-k)*binomial(n, k)*binomial(n, k-1))/n)}

PARI

{a(n) = sum(k=0, n, (-n)^k*(n+1)^(n-k)*binomial(n, k)*binomial(n+k, n)/(k+1))}

Formula

a(n) = Sum_{k=0..n} (-n)^k * (n+1)^(n-k) * binomial(n,k) * binomial(n+k,n)/(k+1).