A368772 a(n) = (n!)^3 * Sum_{k=0..n} (k/k!)^3.

0, 1, 16, 459, 29440, 3680125, 794907216, 272653175431, 139598425821184, 101767252423643865, 101767252423643866000, 135452212975869985647331, 234061424022303335198589696, 514232948577000427431301564309, 1411055210895289172871491492466640

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

a(0) = 0; a(n) = n^3 * a(n-1) + n^3.

a(n) = n^3 * A217284(n-1) for n > 0.

a(n) = Sum_{k=1..n} (k!*binomial(n,k))^3. - Ridouane Oudra, Jun 14 2025

Prog

(PARI) a(n) = n!^3*sum(k=0, n, (k/k!)^3);

Crossrefs

Cf. A368769, A368770, A368771.

Cf. A193563, A217284.

Sequence in context: A241077 A318937 A358569 * A382001 A253446 A159646

Adjacent sequences: A368769 A368770 A368771 * A368773 A368774 A368775

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 05 2024

Status

approved