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 A377583 #14 Nov 02 2024 09:12:53
%S A377583 1,4,20,108,616,3620,21624,129892,778208,4621572,27080680,156080804,
%T A377583 883304976,4905620356,26743018904,143219056740,754280089024,
%U A377583 3911369843204,19995029207496,100885122939172,502952669726960,2480084192804484,12107351426245240,58565261434872548
%N A377583 Expansion of e.g.f. (1 + x * exp(x))^4.
%F A377583 a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(4,k)/(n-k)!.
%F A377583 G.f.: (1 - 36*x + 595*x^2 - 5970*x^3 + 40543*x^4 - 196752*x^5 + 702365*x^6 - 1871250*x^7 + 3740456*x^8 - 5614440*x^9 + 6362360*x^10 - 5588880*x^11 + 3979680*x^12 - 2196672*x^13 + 663552*x^14) / ((1-x)^2*(1-2*x)^3*(1-3*x)^4*(1-4*x)^5).
%o A377583 (PARI) a(n) = n!*sum(k=0, n, k^(n-k)*binomial(4, k)/(n-k)!);
%Y A377583 Cf. A002999, A377582.
%Y A377583 Cf. A377399, A377576.
%K A377583 nonn,easy
%O A377583 0,2
%A A377583 _Seiichi Manyama_, Nov 02 2024