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 A371831 #17 Apr 08 2024 18:49:56
%S A371831 0,1,3,9,31,43,217,3913,9133,73067,1972819,6576067,24112247,372017527,
%T A371831 1612075951,157983443203,7109254944151,37916026368811,644572448269793,
%U A371831 34806912206568841,2422459091299663,7775794614048301,277759159408419360043,2036900502328408640323,46848711553553398727437
%N A371831 a(n) = numerator(Sum_{k=1..n} k^2/k!).
%H A371831 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IncompleteGammaFunction.html">Incomplete Gamma Function</a>.
%H A371831 Wikipedia, <a href="https://en.wikipedia.org/wiki/Incomplete_gamma_function#Upper_incomplete_Gamma_function">Incomplete gamma function</a>.
%F A371831 a(n) = numerator((2*(e*Gamma(n+1, 1) - 1) - n)/n!).
%F A371831 a(n) = numerator(A030297(n)/n!).
%F A371831 Limit_{n->oo} a(n)/A371832(n) = 2*e = A019762.
%t A371831 a[n_]:=Numerator[(2(E*Gamma[n+1,1]-1)-n)/n!]; Array[a,25,0]
%o A371831 (PARI) a(n) = numerator(sum(k=1, n, k^2/k!)); \\ _Michel Marcus_, Apr 07 2024
%Y A371831 Cf. A019762, A030297, A371832.
%Y A371831 Cf. A014973, A092043.
%K A371831 nonn,frac
%O A371831 0,3
%A A371831 _Stefano Spezia_, Apr 07 2024