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 A151649 #13 Sep 23 2022 03:10:38
%S A151649 0,25,182700,84646275,18746073375,3085105337250,443146794326775,
%T A151649 59593466814021450,7756190980563441400,993121304532091347375,
%U A151649 126129019383244869440750,15954027727693152179563525,2014001281330236936094898325,253995299147567448467485168400
%N A151649 Number of permutations of 5 indistinguishable copies of 1..n with exactly 4 adjacent element pairs in decreasing order.
%H A151649 Andrew Howroyd, <a href="/A151649/b151649.txt">Table of n, a(n) for n = 1..200</a>
%H A151649 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (330,-42640,2885620,-114569650,2830998568, -44959643760,466859252380,-3196112991765,14413138051950,-42392995156008, 80058527221680,-95391910308240,69101028551520,-27758817676800,4742523426816).
%F A151649 From _G. C. Greubel_, Sep 12 2022: (Start)
%F A151649 a(n) = Sum_{j=0..4} (-1)^j*binomial(5*n+1, j)*binomial(9-j, 5)^n.
%F A151649 G.f.: 25*x^2*(1 + 6978*x + 1016851*x^2 - 58760395*x^3 - 644809730*x^4 + 39948710783*x^5 - 333333302706*x^6 - 615347004762*x^7 + 9446377773420*x^8 - 24901972278120*x^9 + 4642437947616*x^10 + 51610957036128*x^11 + 7377258663936*x^12)/( Product_{j=0..4} (1 - binomial(j+5, 5)*x)^(5-j) ).
%F A151649 E.g.f.: exp(126*x) - (1 + 280*x)*exp(56*x) + (315/2)*x*(2 + 35*x)*exp(21*x) - 30*x*(4 + 75*x + 150*x^2)*exp(6*x) + (5/24)*x*(72 + 720*x + 700*x^2 + 125*x^3)*exp(x). (End)
%p A151649 a := n -> 126^n - 56^n + 5*(5*n - 2 - 2^(n + 2)*3^n)*(25*n^3 - n)/24 + 5*7^n*n*(5*3^n*n + 3^n - 2^(3*n + 1))/2: seq(a(n), n = 1..14); # _Peter Luschny_, Sep 15 2022
%t A151649 Table[Sum[(-1)^j*Binomial[5*n+1, j]*Binomial[9-j, 5]^n, {j,0,4}], {n, 30}] (* _G. C. Greubel_, Sep 12 2022 *)
%o A151649 (Magma) [(&+[(-1)^j*Binomial(5*n+1, j)*Binomial(9-j, 5)^n: j in [0..4]]): n in [1..30]]; // _G. C. Greubel_, Sep 12 2022
%o A151649 (SageMath)
%o A151649 def A151649(n): return sum((-1)^j*binomial(5*n+1, j)*binomial(9-j, 5)^n for j in (0..4))
%o A151649 [A151649(n) for n in (1..30)] # _G. C. Greubel_, Sep 12 2022
%Y A151649 Column k=4 of A237202.
%K A151649 nonn
%O A151649 1,2
%A A151649 _R. H. Hardin_, May 29 2009
%E A151649 Terms a(7) and beyond from _Andrew Howroyd_, May 06 2020