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 A114253 #20 Sep 06 2025 06:34:04 %S A114253 1,84,3276,92400,2187900,46558512,923410488,17439488352,317907339750, %T A114253 5644249611000,98209943231400,1682207622669600,28457345616827400, %U A114253 476607460678020000,7917519856977720000,130649634333275016960,2143941655711783421340,35018537985874435552560 %N A114253 a(n) = C(5+2*n,5+n)*C(10+2*n,0+n). %H A114253 Robert Israel, <a href="/A114253/b114253.txt">Table of n, a(n) for n = 0..828</a> %F A114253 From _Robert Israel_, Jan 11 2019: (Start) %F A114253 (n+1)^2*(11+n)*a(n+1) = 4*(7+2*n)*(3+n)*(11+2*n)*a(n). %F A114253 a(n) ~ 32768*16^n/(Pi*n). (End) %F A114253 a(n) = A003516(n+2) * A004311(n+5). - _Amiram Eldar_, Sep 06 2025 %e A114253 If n=1 then C(5+2*1,5+1)*C(10+2*1,0+1) = C(7,6)*C(12,1) = 7*12 = 84. %e A114253 If n=11 then C(5+2*n,5+n)*C(10+2*n,0+n) = C(27,16)*C(32,11) = 13037895*129024480 = 1682207622669600. %p A114253 seq(binomial(5+2*n,5+n)*binomial(10+2*n,n),n=0..30); # _Robert Israel_, Jan 11 2019 %t A114253 a[n_] := Binomial[2*n + 5, n + 5]*Binomial[2*n + 10, n]; Array[a, 20, 0] (* _Amiram Eldar_, Sep 06 2025 *) %Y A114253 Cf. A003516, A004311, A062190. %K A114253 easy,nonn,changed %O A114253 0,2 %A A114253 _Zerinvary Lajos_, Feb 04 2006