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 A052181 #22 Sep 06 2024 12:24:48
%S A052181 1,12,72,300,990,2772,6864,15444,32175,62920,116688,206856,352716,
%T A052181 581400,930240,1449624,2206413,3287988,4807000,6906900,9768330,
%U A052181 13616460,18729360,25447500,34184475,45439056,59808672,78004432,100867800,129389040,164727552,208234224
%N A052181 Partial sums of A050483.
%D A052181 Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H A052181 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A052181 a(n) = A027819(n+1)/7.
%F A052181 a(n) = (n+2)*C(n+7, 7)/2.
%F A052181 G.f.: (1+3*x)/(1-x)^9.
%F A052181 a(n) = C(n+2, 2)*C(n+7, 6)/7. - _Zerinvary Lajos_, Jul 29 2005
%F A052181 From _Amiram Eldar_, Feb 11 2022: (Start)
%F A052181 Sum_{n>=0} 1/a(n) = 41783/300 - 14*Pi^2.
%F A052181 Sum_{n>=0} (-1)^n/a(n) = 7*Pi^2 - 2688*log(2)/5 + 91343/300. (End)
%p A052181 a:=n->(sum((numbcomp(n,8)), j=7..n))/2:seq(a(n), n=8..31); # _Zerinvary Lajos_, Aug 26 2008
%t A052181 Table[(n + 2)*Binomial[n + 7, 7]/2, {n, 0, 40}] (* _Amiram Eldar_, Feb 11 2022 *)
%t A052181 LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,12,72,300,990,2772,6864,15444,32175},40] (* _Harvey P. Dale_, Sep 06 2024 *)
%Y A052181 Cf. A027819, A050483.
%Y A052181 Cf. A093561 ((4, 1) Pascal, column m=8).
%K A052181 easy,nonn
%O A052181 0,2
%A A052181 _Barry E. Williams_, Jan 26 2000