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 A151648 #12 Sep 12 2022 03:45:02
%S A151648 0,100,52800,6021225,447069750,28203920250,1662432014600,
%T A151648 95167951614675,5379642996402350,302454892260579500,
%U A151648 16965492408059468000,950717312310731109725,53255101624187593866550,2982626301173304400020350,167034793385579317725373000,9354122482050520106734846375
%N A151648 Number of permutations of 5 indistinguishable copies of 1..n with exactly 3 adjacent element pairs in decreasing order.
%H A151648 Andrew Howroyd, <a href="/A151648/b151648.txt">Table of n, a(n) for n = 1..200</a>
%H A151648 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (120,-5135,105130,-1138875,6873212,-23367945,44115210,-45855180,24607800,-5334336).
%F A151648 a(n) = 56^n - (5*n + 1)*21^n + binomial(5*n+1, 2)*6^n - binomial(5*n+1, 3). - _Andrew Howroyd_, May 07 2020
%F A151648 From _G. C. Greubel_, Sep 12 2022: (Start)
%F A151648 a(n) = Sum_{j=0..3} (-1)^j*binomial(5*n+1, j)*binomial(8-j, 5)^n.
%F A151648 G.f.: 25*x^2*(4 + 1632*x + 7949*x^2 - 594490*x^3 + 1502565*x^4 + 3945816*x^5 - 13945932*x^6 - 4667544*x^7)/( Product_{j=0.3} (1 - binomial(j+5, 5)*x)^(4-j) ).
%F A151648 E.g.f.: exp(56*x) - (1 + 105*x)*exp(21*x) + 90*x*(1 + 5*x)*exp(6*x) - (5/6)*x*(24 + 75*x + 25*x^2)*exp(x). (End)
%t A151648 Table[Sum[(-1)^j*Binomial[5*n+1, j]*Binomial[8-j, 5]^n, {j,0,3}], {n, 30}] (* _G. C. Greubel_, Sep 12 2022 *)
%o A151648 (PARI) a(n) = {56^n - (5*n + 1)*21^n + binomial(5*n+1, 2)*6^n - binomial(5*n+1, 3)} \\ _Andrew Howroyd_, May 07 2020
%o A151648 (Magma) [(&+[(-1)^j*Binomial(5*n+1, j)*Binomial(8-j, 5)^n: j in [0..3]]): n in [1..30]]; // _G. C. Greubel_, Sep 12 2022
%o A151648 (SageMath)
%o A151648 def A151648(n): return sum((-1)^j*binomial(5*n+1, j)*binomial(8-j, 5)^n for j in (0..3))
%o A151648 [A151648(n) for n in (1..30)] # _G. C. Greubel_, Sep 12 2022
%Y A151648 Column k=3 of A237202.
%K A151648 nonn
%O A151648 1,2
%A A151648 _R. H. Hardin_, May 29 2009
%E A151648 Terms a(8) and beyond from _Andrew Howroyd_, May 07 2020