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 A378854 #21 Feb 21 2025 07:20:10
%S A378854 3,9,24,51,111,213,414,756,1374,2409,4206,7152,12096,20109,33198,
%T A378854 54111,87648,140520,223953,354006,556419,868584,1348857,2082225,
%U A378854 3198927,4888944,7438548,11265141,16990077,25516401,38175240,56894490,84490935,125028489,184400952
%N A378854 a(n) is the number of solid (3D) partitions of n with 2 layers and second layer a plane partition of 2.
%C A378854 Appears to equal 3*A097391(n-3).
%H A378854 Wouter Meeussen <a href="/A094504/a094504_1.txt">Mma functions for plane and solid partitions</a>
%F A378854 From _John Tyler Rascoe_, Feb 20 2025: (Start)
%F A378854 a(n) = 3*(A000219(n-2) - A000041(n-2)).
%F A378854 G.f.: 3*x^2 * (Product_{i>0} (1/(1-x^i)^i) - Product_{i>0} (1/(1-x^i)^i)). (End)
%e A378854 a(4)=3 since the 3 solid partitions of {2,2} are:
%e A378854 [{{2}},{{2}}], [{{1,1}},{{1,1}}], [{{1},{1}},{{1},{1}}]
%e A378854 a(5)=9 since the 9 solid partitions of {3,2} are:
%e A378854 [{{3}},{{2}}], [{{2,1}},{{2}}], [{{2,1}},{{1,1}}], [{{1,1,1}},{{1,1}}], [{{2},{1}},{{2}}], [{{2},{1}},{{1},{1}}],[{{1,1},{1}},{{1,1}}], [{{1,1},{1}},{{1},{1}}], [{{1},{1},{1}},{{1},{1}}]
%t A378854 Table[Length@solidformBTK[{n-2,2}],{n,4,22}] (* uses functions defined in link above *)
%o A378854 (PARI)
%o A378854 A_x(N) = {my(x='x+O('x^N)); Vec(3*x^2*(prod(i=1,N, 1/(1-x^i)^i)-prod(i=1,N, 1/(1-x^i))))}
%o A378854 A_x(40) \\ _John Tyler Rascoe_, Feb 20 2025
%Y A378854 Cf. A097391, A094504, A000219, A000041.
%K A378854 nonn
%O A378854 4,1
%A A378854 _Wouter Meeussen_, Feb 10 2025
%E A378854 a(23) onwards from _John Tyler Rascoe_, Feb 20 2025