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 A371079 #10 Mar 12 2024 22:47:32
%S A371079 1,1,2,7,42,383,4716,72831,1349302,29123127,717194888,19837095511,
%T A371079 608717233346,20518453925807,753563361399012,29948045451609743,
%U A371079 1280446573813600366,58602977409168609351,2858550564643752169312,148037904246807129342247,8111929349028033318115898
%N A371079 a(n) = Sum_{k=0..n} 3^(n - k)*Pochhammer(k/3, n - k). Row sums of A371077.
%F A371079 From _Vaclav Kotesovec_, Mar 12 2024: (Start)
%F A371079 Recurrence: (n-6)*(3*n - 14)*a(n) = (27*n^3 - 375*n^2 + 1690*n - 2465)*a(n-1) - (81*n^4 - 1458*n^3 + 9726*n^2 - 28519*n + 31035)*a(n-2) + (81*n^5 - 1836*n^4 + 16542*n^3 - 74055*n^2 + 164751*n - 145753)*a(n-3) - (81*n^5 - 1998*n^4 + 19557*n^3 - 94944*n^2 + 228592*n - 218342)*a(n-4) - 2*(3*n - 11)*(9*n^3 - 129*n^2 + 611*n - 957)*a(n-5) + 2*(n-5)*(3*n - 16)*(3*n - 14)*(3*n - 11)*a(n-6).
%F A371079 a(n) ~ sqrt(2*Pi) * 3^(n-1) * n^(n - 7/6) / (Gamma(1/3) * exp(n)) * (1 + Gamma(1/3)^2 / (2*Pi*sqrt(3)*n^(2/3))). (End)
%p A371079 a := n -> local k; add(3^(n - k)*pochhammer(k/3, n - k), k = 0..n):
%p A371079 seq(a(n), n = 0..20);
%t A371079 Table[Sum[3^(n-k) * Pochhammer[k/3, n-k], {k, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, Mar 12 2024 *)
%Y A371079 Cf. A371077, A370982, A000522.
%K A371079 nonn,easy
%O A371079 0,3
%A A371079 _Peter Luschny_, Mar 12 2024