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 A377582 #12 Nov 02 2024 09:12:49
%S A377582 1,3,12,51,228,1035,4698,21063,92424,395091,1643790,6664383,26387100,
%T A377582 102286587,389125506,1455994935,5368721808,19541252259,70312410774,
%U A377582 250408115823,883617559140,3092276105163,10740749281482,37053754521831,127037475064728,433073722098675
%N A377582 Expansion of e.g.f. (1 + x * exp(x))^3.
%F A377582 a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(3,k)/(n-k)!.
%F A377582 G.f.: (1-17*x+127*x^2-542*x^3+1453*x^4-2543*x^5+2973*x^6-2478*x^7+1626*x^8-648*x^9) / ((1-x)^2*(1-2*x)^3*(1-3*x)^4).
%o A377582 (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(3, k)/(n-k)!);
%Y A377582 Cf. A002999, A377583.
%Y A377582 Cf. A001815, A052791.
%Y A377582 Cf. A377530, A377575.
%K A377582 nonn,easy
%O A377582 0,2
%A A377582 _Seiichi Manyama_, Nov 02 2024