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 A151626 #18 Jun 11 2023 11:43:37
%S A151626 0,0,1,603,47290,1822014,49258935,1086859301,21147576440,379269758400,
%T A151626 6441229796061,105398150289775,1680774708581766,26324724399068626,
%U A151626 407112461900381715,6239897666881158537,95036195852840662820,1440959515956284422196,21778829725476446172249
%N A151626 Number of permutations of 2 indistinguishable copies of 1..n with exactly 4 adjacent element pairs in decreasing order.
%H A151626 Andrew Howroyd, <a href="/A151626/b151626.txt">Table of n, a(n) for n = 1..200</a>
%H A151626 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (70, -2163, 39122, -462914, 3792972, -22214806, 94629124, -295393077, 675442494, -1122134391, 1331169066, -1093400856, 588623760, -186332400, 26244000).
%F A151626 a(n) = 15^n - (2*n + 1)*10^n + binomial(2*n+1, 2)*6^n - binomial(2*n+1, 3)*3^n + binomial(2*n+1, 4). - _Andrew Howroyd_, May 07 2020
%F A151626 From _G. C. Greubel_, Sep 07 2022: (Start)
%F A151626 G.f.: x^3*(1 + 533*x + 7243*x^2 - 223119*x^3 + 878573*x^4 + 5014923*x^5 - 40074183*x^6 + 75062403*x^7 + 19732086*x^8 - 185394420*x^9 + 117543960*x^10 + 43740000*x^11)/((1-x)^5*(1-3*x)^4*(1-6*x)^3*(1-10*x)^2*(1-15*x)).
%F A151626 E.g.f.: exp(15*x) - (1+20*x)*exp(10*x) + 18*x*(1+4*x)*exp(6*x) - 3*x*(1 + 12*x + 12*x^2)*exp(3*x) + (x^2/6)*(15 + 20*x + 4*x^2)*exp(x). (End)
%t A151626 With[{B=Binomial}, Table[Sum[(-1)^(j+1)*B[2n+1, 5-j]*B[j+1,2]^n, {j,5}], {n,30}]] (* _G. C. Greubel_, Sep 07 2022 *)
%o A151626 (PARI) a(n) = {15^n - (2*n + 1)*10^n + binomial(2*n+1, 2)*6^n - binomial(2*n+1, 3)*3^n + binomial(2*n+1, 4) } \\ _Andrew Howroyd_, May 07 2020
%o A151626 (Magma)
%o A151626 A151626:= func< n | (&+[(-1)^(j+1)*Binomial(2*n+1,5-j)*Binomial(j+1,2)^n: j in [1..5]]) >;
%o A151626 [A151626(n): n in [1..30]]; // _G. C. Greubel_, Sep 07 2022
%o A151626 (SageMath)
%o A151626 @CachedFunction
%o A151626 def A151626(n): return sum((-1)^(j+1)*binomial(2*n+1,5-j)*binomial(j+1,2)^n for j in (1..5))
%o A151626 [A151626(n) for n in (1..30)] # _G. C. Greubel_, Sep 07 2022
%Y A151626 Column k=4 of A154283.
%K A151626 nonn
%O A151626 1,4
%A A151626 _R. H. Hardin_, May 29 2009
%E A151626 Terms a(12) and beyond from _Andrew Howroyd_, May 07 2020