A374616 -id:A374616 - cp's OEIS frontend

A374614 a(n) = Sum_{k=0..n} (k/n)^2 * binomial(n,k)^5.

1, 9, 136, 2585, 54126, 1227492, 29226688, 723533337, 18438032890, 480994824134, 12787403151744, 345355150592036, 9451729196625184, 261628075707534720, 7313361005558843136, 206190939973811373593, 5857313490484652859282

Offset: 1

Seiichi Manyama, Jul 14 2024

nonn

Cf. A005261, A374615, A374616.

Cf. A181067, A198256.

Table[Sum[(k/n)^2 Binomial[n,k]^5,{k,0,n}],{n,20}] (* Harvey P. Dale, Jun 16 2025 *)

a(n) = sum(k=0, n-1, binomial(n-1, k)^2*binomial(n, k)^3);

a(n) = Sum_{k=0..n-1} binomial(n-1,k)^2 * binomial(n,k)^3.

A374615 a(n) = Sum_{k=0..n} (k/n)^3 * binomial(n,k)^5.

Original entry on oeis.org

1, 5, 82, 1421, 29626, 657662, 15528640, 381137549, 9656742322, 250689517130, 6638957500924, 178721359853390, 4878005765458528, 134712060315562784, 3758101325718600832, 105769714118196065933, 3000003700599260555650, 85677293959381174518986

Offset: 1

Seiichi Manyama, Jul 14 2024

nonn

Cf. A005261, A374614, A374616.

Cf. A181069.

a(n) = sum(k=0, n-1, binomial(n-1, k)^3*binomial(n, k)^2);

a(n) = Sum_{k=0..n-1} binomial(n-1,k)^3 * binomial(n,k)^2.

cp's OEIS Frontend

A374614 a(n) = Sum_{k=0..n} (k/n)^2 * binomial(n,k)^5.

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