This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A076483 #16 Jul 15 2023 10:35:38
%S A076483 0,0,1,11,125,1649,25519,458569,9433353,219117905,5677963451,
%T A076483 162457597961,5087919552253,173136159558361,6361282619516343,
%U A076483 250987334850557369,10584205713321808529,475079402305823570849,22614513693572549266291,1137911105533216112417161
%N A076483 a(n) = n!*Sum_{k=1..n} (k-1)^k/k!.
%C A076483 Perhaps the largest possible number of ways of choosing (v1, v2, ..., vn), possibly with repetition, from {b1, b2, ..., bn} with b1 < b2 < ... < bn, such that v1 + v2 + ... + vn < b1 + b2 + ... + bn. Clearly the actual number of ways depends on the particular values of {b1, b2, ..., bn}, but {1, n, n^2, ..., n^(n-1)} produces this result for the number of sums strictly less than (n^n-1)/(n-1) = A023037(n).
%H A076483 Seiichi Manyama, <a href="/A076483/b076483.txt">Table of n, a(n) for n = 0..386</a>
%F A076483 Limit_{n->oo} a(n)/(e*a(n-1)) - n = -1/2.
%F A076483 Limit_{n->oo} a(n)/n^n = 1/(e-1).
%e A076483 a(4) = 4!*(0^1/1! + 1^2/2! + 2^3/3! + 3^4/4!) = 0 + 12 + 32 + 81 = 125.
%t A076483 Table[n! Sum[(k-1)^k/k!, {k,n}], {n,0,17}] (* _Stefano Spezia_, Sep 11 2022 *)
%o A076483 (PARI) a(n) = n!*sum(k=1, n, (k-1)^k/k!); \\ _Seiichi Manyama_, Jul 15 2023
%Y A076483 Row sums of A076482.
%Y A076483 Cf. A023037, A075473.
%K A076483 nonn
%O A076483 0,4
%A A076483 _Henry Bottomley_, Oct 14 2002