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 A360934 #13 Feb 26 2023 08:42:38 %S A360934 1,1,7,73,1711,75121,6743287,1169659513,412296162271,284887781497441, %T A360934 400134611520973927,1108533158650520901673,6238465090832886119430031, %U A360934 69421876683500992783472318161,1567475216919199483376363835235927 %N A360934 Expansion of e.g.f. Sum_{k>=0} exp((4^k - 1)*x) * x^k/k!. %F A360934 G.f.: Sum_{k>=0} x^k/(1 - (4^k - 1)*x)^(k+1). %F A360934 a(n) = Sum_{k=0..n} (4^k - 1)^(n-k) * binomial(n,k). %o A360934 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1+sum(k=1, N, exp((4^k-1)*x)*x^k/k!))) %o A360934 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k/(1-(4^k-1)*x)^(k+1))) %o A360934 (PARI) a(n) = sum(k=0, n, (4^k-1)^(n-k)*binomial(n, k)); %Y A360934 Cf. A001831, A360933, A360935. %Y A360934 Cf. A135754, A355440. %K A360934 nonn,easy %O A360934 0,3 %A A360934 _Seiichi Manyama_, Feb 26 2023