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 A020922 #31 Mar 25 2022 09:13:42
%S A020922 1,22,286,2860,24310,184756,1293292,8498776,53117350,318704100,
%T A020922 1848483780,10418726760,57302997180,308554600200,1630931458200,
%U A020922 8480843582640,43464323361030,219878341708740,1099391708543700,5439095821216200,26651569523959380,129450480544945560
%N A020922 Expansion of 1/(1-4*x)^(11/2).
%C A020922 Also convolution of A000984 with A040075, also convolution of A000302 with A020920, also convolution of A002457 with A038846, also convolution of A002697 with A020918, also convolution of A002802 with A038845. - _Rui Duarte_, Oct 08 2011
%H A020922 Vincenzo Librandi, <a href="/A020922/b020922.txt">Table of n, a(n) for n = 0..200</a>
%F A020922 a(n) = binomial(n+5, 5)*A000984(n+5)/A000984(5), where A000984 are central binomial coefficients. - _Wolfdieter Lang_
%F A020922 From _Rui Duarte_, Oct 08 2011: (Start)
%F A020922 a(n) = ((2n+9)(2n+7)(2n+5)(2n+3)(2n+1)/(9*7*5*3*1)) * binomial(2n, n).
%F A020922 a(n) = binomial(2n+10, 10) * binomial(2n, n) / binomial(n+5, 5).
%F A020922 a(n) = binomial(n+5, 5) * binomial(2n+10, n+5) / binomial(10, 5).
%F A020922 a(n) = Sum_{ i_1+i_2+i_3+i_4+i_5+i_6+i_7+i_8+i_9+i_10+i_11 = n } f(i_1)* f(i_2)*f(i_3)*f(i_4)*f(i_5)*f(i_6)*f(i_7)*f(i_8)*f(i_9)*f(i_10)*f(i_11) with f(k)=A000984(k). (End)
%F A020922 Boas-Buck recurrence: a(n) = (22/n)*Sum_{k=0..n-1} 4^(n-k-1)*a(k), n >= 1, a(0) = 1. Proof from a(n) = A046521(n+5, 5). See a comment there. - _Wolfdieter Lang_, Aug 10 2017
%F A020922 From _Amiram Eldar_, Mar 25 2022: (Start)
%F A020922 Sum_{n>=0} 1/a(n) = 162*sqrt(3)*Pi - 30816/35.
%F A020922 Sum_{n>=0} (-1)^n/a(n) = 4500*sqrt(5)*log(phi) - 33888/7, where phi is the golden ratio (A001622). (End)
%t A020922 CoefficientList[Series[1/(1-4x)^(11/2), {x,0,30}], x] (* _Vincenzo Librandi_, Jul 05 2013 *)
%o A020922 (Magma) [(2*n+9)*(2*n+7)*(2*n+5)*(2*n+3)*(2*n+1)*Binomial(2*n, n)/945: n in [0..30]] // _Vincenzo Librandi_, Jul 05 2013
%o A020922 (PARI) vector(30, n, n--; m=n+5; binomial(m, 5)*binomial(2*m, m)/252) \\ _G. C. Greubel_, Jul 20 2019
%o A020922 (Sage) [binomial(n+5, 5)*binomial(2*n+10, n+5)/252 for n in (0..30)] # _G. C. Greubel_, Jul 20 2019
%o A020922 (GAP) List([0..30], n-> Binomial(n+5, 5)*Binomial(2*n+10, n+5)/252); # _G. C. Greubel_, Jul 20 2019
%Y A020922 Cf. A000302, A000984, A001622, A002457, A002697, A002802, A020918, A020920, A038845, A038846, A040075, A046521 (sixth column).
%K A020922 nonn,easy
%O A020922 0,2
%A A020922 _N. J. A. Sloane_