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 A151633 #12 Jun 11 2023 11:53:46
%S A151633 0,1,760,49682,1722320,45699447,1063783164,23119658500,484099087156,
%T A151633 9930487583345,201402352998560,4059011173618086,81520052344904040,
%U A151633 1634100242397204427,32722001111322772660,654870005050881521672,13102000022780506515884
%N A151633 Number of permutations of 3 indistinguishable copies of 1..n with exactly 3 adjacent element pairs in decreasing order.
%H A151633 Andrew Howroyd, <a href="/A151633/b151633.txt">Table of n, a(n) for n = 1..200</a>
%H A151633 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (56, -1242, 14412, -96873, 394308, -984324, 1492224, -1330560, 640000, -128000).
%F A151633 a(n) = 20^n - (3*n + 1)*10^n + binomial(3*n+1, 2)*4^n - binomial(3*n+1, 3). - _Andrew Howroyd_, May 07 2020
%F A151633 a(n) = Sum_{j=0..5} (-1)^(j+1)*binomial(3*n+1, 5-j)*(binomial(j+1, 3))^n. - _G. C. Greubel_, Mar 26 2022
%t A151633 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 A151633 Table[T[n, 3], {n, 30}] (* _G. C. Greubel_, Mar 26 2022 *)
%o A151633 (PARI) a(n) = {20^n - (3*n + 1)*10^n + binomial(3*n+1, 2)*4^n - binomial(3*n+1, 3)} \\ _Andrew Howroyd_, May 07 2020
%o A151633 (Sage)
%o A151633 @CachedFunction
%o A151633 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 A151633 [T(n, 3) for n in (1..30)] # _G. C. Greubel_, Mar 26 2022
%Y A151633 Column k=3 of A174266.
%K A151633 nonn
%O A151633 1,3
%A A151633 _R. H. Hardin_, May 29 2009
%E A151633 Terms a(10) and beyond from _Andrew Howroyd_, May 07 2020