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 A320432 #80 Jul 06 2020 20:44:29 %S A320432 1,-2,1,7,-8,-65,37,1024,1351,-19001,-92618,232513,4087189,9953926, %T A320432 -123909155,-1170342533,-676144160,62840385619,490129709977, %U A320432 -551829062288,-40624407525941,-305175084654341,698633855671510,34571970743398621,278738497423756153,-663168571756087538 %N A320432 Expansion of e.g.f. exp(3 * (1 - exp(x)) + x). %F A320432 a(0) = 1 and a(n) = a(n-1) - 3 * Sum_{k=0..n-1} binomial(n-1,k) * a(k) for n > 0. %F A320432 a(n) = exp(3) * Sum_{k>=0} (k + 1)^n * (-3)^k / k!. %F A320432 a(n) = Sum_{k=0..n} binomial(n,k) * Bell(k, -3). - _Vaclav Kotesovec_, Jul 06 2020 %t A320432 m = 25; Range[0, m]! * CoefficientList[Series[Exp[3 * (1 - Exp[x]) + x], {x, 0, m}], x] (* _Amiram Eldar_, Jul 06 2020 *) %t A320432 Table[Sum[Binomial[n, k] * BellB[k, -3], {k, 0, n}], {n, 0, 30}] (* _Vaclav Kotesovec_, Jul 06 2020 *) %o A320432 (PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(3*(1-exp(x))+x))) %Y A320432 Column k=3 of A335977. %Y A320432 Cf. A078940, A335981. %K A320432 sign %O A320432 0,2 %A A320432 _Seiichi Manyama_, Jul 06 2020