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 A081900 #17 Mar 22 2025 12:27:17
%S A081900 1,9,71,519,3606,24150,157250,1001250,6259375,38534375,234140625,
%T A081900 1406640625,8367187500,49335937500,288632812500,1676757812500,
%U A081900 9678955078125,55548095703125,317108154296875,1801483154296875,10188293457031250,57380676269531250,321922302246093750
%N A081900 Fourth binomial transform of binomial(n+4, 4).
%C A081900 Binomial transform of A081899.
%C A081900 5th binomial transform of (1,4,6,4,1,0,0,0,...).
%H A081900 G. C. Greubel, <a href="/A081900/b081900.txt">Table of n, a(n) for n = 0..1000</a>
%H A081900 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (25,-250,1250,-3125,3125).
%F A081900 a(n) = 5^n*(n^4 + 74*n^3 + 1571*n^2 + 10354*n + 15000)/15000.
%F A081900 G.f.: (1 - 4*x)^4/(1 - 5*x)^5.
%F A081900 E.g.f.: (24 + 96*x + 72*x^2 + 16*x^3 + x^4)*exp(5*x)/24. - _G. C. Greubel_, Oct 18 2018
%t A081900 LinearRecurrence[{25,-250,1250,-3125,3125}, {1,9,71,519,3606}, 50] (* _G. C. Greubel_, Oct 18 2018 *)
%o A081900 (PARI) x='x+O('x^30); Vec((1-4*x)^4/(1-5*x)^5) \\ _G. C. Greubel_, Oct 18 2018
%o A081900 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-4*x)^4/(1-5*x)^5)); // _G. C. Greubel_, Oct 18 2018
%Y A081900 Cf. A000332, A081899.
%K A081900 nonn,easy
%O A081900 0,2
%A A081900 _Paul Barry_, Mar 31 2003