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 A227995 #20 Apr 04 2017 03:16:04
%S A227995 1,3,25,195,1625,13879,120717,1063323,9454977,84688303,762972225,
%T A227995 6906366907,62762167561,572251392039,5232480571761,47961608620959,
%U A227995 440565328458621,4054586252967027,37377503512616413,345083448151227987,3190232694060946333,29529002023029712547
%N A227995 Alternate partial sums of the binomial coefficients C(4*n,n).
%C A227995 Generally (for p>1), alternate partial sums of the binomial coefficients C(p*n,n) is asymptotic to (1/(1+(p-1)^(p-1)/p^p)) * sqrt(p/(2*Pi*n*(p-1))) * (p^p/(p-1)^(p-1))^n.
%H A227995 G. C. Greubel, <a href="/A227995/b227995.txt">Table of n, a(n) for n = 0..1000</a>
%F A227995 Recurrence: 3*n*(3*n-2)*(3*n-1)*a(n) = (229*n^3 - 357*n^2 + 170*n - 24)*a(n-1) + 8*(2*n-1)*(4*n-3)*(4*n-1)*a(n-2).
%F A227995 a(n) ~ 2^(8*n+17/2)/(283*sqrt(Pi*n)*3^(3*n+1/2)).
%t A227995 Table[Sum[Binomial[4*k, k]*(-1)^(n-k), {k, 0, n}], {n, 0, 20}]
%o A227995 (PARI) for(n=0,50, print1(sum(k=0,n, binomial(4*k,k)), ", ")) \\ _G. C. Greubel_, Apr 03 2017
%Y A227995 Cf. A054108(n-1) (p=2), A188676 (p=3), A227996 (p=5).
%K A227995 nonn,easy
%O A227995 0,2
%A A227995 _Vaclav Kotesovec_, Aug 06 2013