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