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 A382349 #19 May 23 2025 03:08:00
%S A382349 1,7,146,4578,189144,9660840,586813968,41283943344,3299858098560,
%T A382349 295294500123840,29242449106502400,3174506423754019200,
%U A382349 374845813851886709760,47828682507084551654400,6557612642418946942310400,961431335221085133398784000,150095351600371197275428454400
%N A382349 a(n) = [x^n] Product_{k=0..n} (1 + (3*n+k)*x).
%F A382349 a(n) = A165675(4*n,3*n).
%F A382349 a(n) = Sum_{k=0..n} (k+1) * (3*n)^k * |Stirling1(n+1,k+1)|.
%F A382349 a(n) = (n+1)! * Sum_{k=0..n} (-1)^k * binomial(-3*n,k)/(n+1-k).
%F A382349 a(n) = (4*n)!/(3*n)! * (1 + 3*n * Sum_{k=1..n} 1/(3*n+k)).
%F A382349 a(n) ~ log(4/3) * 2^(8*n+1) * n^(n+1) / (exp(n) * 3^(3*n - 1/2)). - _Vaclav Kotesovec_, May 23 2025
%t A382349 Table[SeriesCoefficient[Product[(1 + (3*n+k)*x), {k, 0, n}], {x, 0, n}], {n, 0, 20}] (* _Vaclav Kotesovec_, May 23 2025 *)
%o A382349 (PARI) a(n) = sum(k=0, n, (k+1)*(3*n)^k*abs(stirling(n+1, k+1, 1)));
%Y A382349 Column k=3 of A382347.
%Y A382349 Cf. A165675.
%K A382349 nonn
%O A382349 0,2
%A A382349 _Seiichi Manyama_, May 18 2025