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 A151635 #12 Jun 11 2023 11:55:45
%S A151635 0,0,54,128124,40241088,5904797049,592030140912,47871255785661,
%T A151635 3399596932632516,222507204130403730,13816730633213564154,
%U A151635 828855022115369147634,48598186867956968680368,2806334420165022553155783,160409202733612103932779012,9106532681255976991378628043
%N A151635 Number of permutations of 3 indistinguishable copies of 1..n with exactly 5 adjacent element pairs in decreasing order.
%H A151635 Andrew Howroyd, <a href="/A151635/b151635.txt">Table of n, a(n) for n = 1..200</a>
%H A151635 <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (252, -28116, 1847460, -80186430, 2443408020, -54222394300, 897042522780, -11233051883145, 107495660310160, -790365294823704, 4473663278780448, -19473246213545104, 64926170063690880, -164639495047219200, 314180023114240000, -444424489989120000, 455945899622400000, -328038555648000000, 156378808320000000, -44255232000000000, 5619712000000000).
%F A151635 a(n) = Sum_{j=0..7} (-1)^(j+1)*binomial(3*n+1, 7-j)*(binomial(j+1, 3))^n. - _G. C. Greubel_, Mar 26 2022
%t A151635 T[n_, k_]:= T[n, k]= Sum[(-1)^(k-j)*Binomial[3*n+1, k-j+2]*(Binomial[j+1,3])^n, {j, 0, k+2}];
%t A151635 Table[T[n, 5], {n, 30}] (* _G. C. Greubel_, Mar 26 2022 *)
%o A151635 (Sage)
%o A151635 @CachedFunction
%o A151635 def T(n, k): return sum( (-1)^(k-j)*binomial(3*n+1, k-j+2)*(binomial(j+1,3))^n for j in (0..k+2) )
%o A151635 [T(n, 5) for n in (1..30)] # _G. C. Greubel_, Mar 26 2022
%Y A151635 Column k=5 of A174266.
%K A151635 nonn
%O A151635 1,3
%A A151635 _R. H. Hardin_, May 29 2009
%E A151635 Terms a(9) and beyond from _Andrew Howroyd_, May 06 2020