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 A360933 #17 Feb 26 2023 06:56:17 %S A360933 1,1,5,37,521,12361,510605,35837677,4348414481,903630399121, %T A360933 325415100648725,201805338104622517,217331913727442676761, %U A360933 404193405278758441895641,1306527408146744068362681245,7302236837745565755664036677757 %N A360933 Expansion of e.g.f. Sum_{k>=0} exp((3^k - 1)*x) * x^k/k!. %F A360933 G.f.: Sum_{k>=0} x^k/(1 - (3^k - 1)*x)^(k+1). %F A360933 a(n) = Sum_{k=0..n} (3^k - 1)^(n-k) * binomial(n,k). %o A360933 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1+sum(k=1, N, exp((3^k-1)*x)*x^k/k!))) %o A360933 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(3^k-1)*x)^(k+1))) %o A360933 (PARI) a(n) = sum(k=0, n, (3^k-1)^(n-k)*binomial(n, k)); %Y A360933 Cf. A001831, A360934, A360935. %Y A360933 Cf. A135079, A135753. %K A360933 nonn,easy %O A360933 0,3 %A A360933 _Seiichi Manyama_, Feb 26 2023