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 A379877 #29 Jan 23 2025 12:57:24
%S A379877 1,0,1,2,33,244,4345,61830,1332961,28087208,739562481,20380504330,
%T A379877 644853623425,21767589641628,810480865644073,32246095869576974,
%U A379877 1385625666085792065,63366863108725330000,3090966367543869021409,159607809547688836085778,8718178798812199357657441
%N A379877 E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^2) + x*A(x)^3.
%H A379877 <a href="https://dlmf.nist.gov/13.2">Kummer Functions</a>, Digital Library of Mathematical Functions, Jan. 2025.
%F A379877 a(n) = -n! * Sum_{k=0..n} (-2*n-1)^(n-k-1) * binomial(2*n+k, k) / (n-k)!.
%F A379877 a(n) = U(-n, -3*n, -1 - 2*n)/(1 + 2*n), where U is the Kummer U function. - _David Trimas_, Jan 09 2025
%F A379877 a(n) ~ 2^(3*n) * n^(n-1) / (sqrt(3) * exp(2*n + 1/2)). - _Vaclav Kotesovec_, Jan 15 2025
%t A379877 Table[-n! * Sum[(-2*n - 1)^(n-k-1) * Binomial[2*n + k, k]/(n-k)!, {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jan 15 2025 *)
%o A379877 (PARI) a(n) = -n!*sum(k=0, n, (-2*n-1)^(n-k-1)*binomial(2*n+k, k)/(n-k)!);
%Y A379877 Cf. A379871, A379876, A379878.
%K A379877 nonn
%O A379877 0,4
%A A379877 _Seiichi Manyama_, Jan 05 2025