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 A081904 #18 Mar 22 2025 13:31:31
%S A081904 1,9,60,344,1794,8754,40636,181380,784251,3302451,13598280,54922860,
%T A081904 218131380,853586100,3296508840,12581531064,47510175861,177681098205,
%U A081904 658665849636,2422018974096,8840103322374,32044237392726,115417729279620,413255236888476,1471500113899311
%N A081904 Second binomial transform of binomial(n+6, 6).
%C A081904 Binomial transform of A055853 (without leading 0).
%C A081904 3rd binomial transform of (1,6,15,20,15,6,1,0,0,0,...).
%H A081904 G. C. Greubel, <a href="/A081904/b081904.txt">Table of n, a(n) for n = 0..1000</a>
%H A081904 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (21,-189,945,-2835,5103,-5103, 2187).
%F A081904 a(n) = 3^n*(n^6 + 93*n^5 + 3055*n^4 + 44055*n^3 + 282424*n^2 + 720132*n + 524880)/524880.
%F A081904 G.f.: (1 - 2*x)^6/(1 - 3*x)^7.
%F A081904 E.g.f.: (720 + 4320*x + 5400*x^2 + 2400*x^3 + 450*x^4 + 36*x^5 + x^6)*exp(3*x) / 720. - _G. C. Greubel_, Oct 18 2018
%t A081904 LinearRecurrence[{21,-189,945,-2835,5103,-5103,2187}, {1,9,60,344,1794, 8754,40636}, 50] (* _G. C. Greubel_, Oct 18 2018 *)
%o A081904 (PARI) x='x+O('x^30); Vec((1-2*x)^6/(1-3*x)^7) \\ _G. C. Greubel_, Oct 18 2018
%o A081904 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x)^6/(1-3*x)^7)); // _G. C. Greubel_, Oct 18 2018
%Y A081904 Cf. A000579, A055853, A081905.
%K A081904 nonn,easy
%O A081904 0,2
%A A081904 _Paul Barry_, Mar 31 2003