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 A123614 #12 Feb 04 2023 13:32:25
%S A123614 1,5,39,175,618,1764,4420,9900,20439,39325,71603,124215,207076,333200,
%T A123614 520272,790704,1173805,1705725,2432375,3409175,4704846,6400900,
%U A123614 8596484,11407500,14972643,19452069,25034835,31936975,40410504,50740800,63257408,78330560
%N A123614 Column 4 of triangle A123610.
%H A123614 G. C. Greubel, <a href="/A123614/b123614.txt">Table of n, a(n) for n = 0..1000</a>
%H A123614 <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-4,12,-12,4,12,-22,12,4,-12,12,-4,-4,4,-1).
%F A123614 G.f.: P_4(x) / ((1-x)^2*(1-x^2)^2*(1-x^3)^2*(1-x^4)^2), with P_4(1) = 7!, where P_4(x) = (1+3*x+28*x^2+94*x^3+240*x^4+440*x^5+679*x^6+839*x^7+ 887*x^8+757*x^9+550*x^10+314*x^11+148*x^12+48*x^13+11*x^14+x^15).
%t A123614 CoefficientList[Series[(1 + 3*x + 28*x^2 + 94*x^3 + 240*x^4 + 440*x^5 + 679*x^6 + 839*x^7 + 887*x^8 + 757*x^9 + 550*x^10 + 314*x^11 + 148*x^12 + 48*x^13 + 11*x^14 + x^15)/((1 - x)^2*(1 - x^2)^2*(1 - x^3)^2*(1 - x^4)^2), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 16 2017 *)
%t A123614 LinearRecurrence[{4,-4,-4,12,-12,4,12,-22,12,4,-12,12,-4,-4,4,-1},{1,5,39,175,618,1764,4420,9900,20439,39325,71603,124215,207076,333200,520272,790704},40] (* _Harvey P. Dale_, Feb 04 2023 *)
%o A123614 (PARI) {a(n)=polcoeff(truncate(Ser([1,3,28,94,240,440,679,839,887,757,550,314,148,48,11,1]))/ ((1-x)^2*(1-x^2)^2*(1-x^3)^2*(1-x^4)^2 +x*O(x^n)),n)}
%Y A123614 Cf. A123610 (triangle); columns: A005997, A123613, A123615, A123616.
%K A123614 nonn,easy
%O A123614 0,2
%A A123614 _Paul D. Hanna_, Oct 03 2006