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 A368575 #10 Dec 31 2023 10:22:48 %S A368575 0,1,7,36,179,965,5916,41622,333306,3000249,30003205,330036256, %T A368575 3960436437,51485675501,720799459394,10811991893970,172991870307396, %U A368575 2940861795230577,52935512314156371,1005774733968978364,20115494679379576135,422425388266971109461 %N A368575 a(n) = n! * Sum_{k=0..n} binomial(k+3,4) / k!. %F A368575 a(0) = 0; a(n) = n*a(n-1) + binomial(n+3,4). %F A368575 E.g.f.: x * (1+3*x/2+x^2/2+x^3/24) * exp(x) / (1-x). %o A368575 (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 3, binomial(3, k)*x^k/(k+1)!)*exp(x)/(1-x)))) %Y A368575 Cf. A007526, A103519, A368574, A368576. %Y A368575 Cf. A000332, A337002. %K A368575 nonn,easy %O A368575 0,3 %A A368575 _Seiichi Manyama_, Dec 31 2023