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 A240876 #66 Jan 05 2023 18:27:30
%S A240876 1,23,265,2047,11969,56695,227305,795455,2485825,7059735,18474633,
%T A240876 45046719,103274625,224298231,464387817,921406335,1759885185,
%U A240876 3248227095,5812626185,10113604735,17152640321,28418229623,46082942185,73265596607,114375683009
%N A240876 Expansion of (1 + x)^11 / (1 - x)^12.
%C A240876 Also 11-dimensional centered hyperoctahedron numbers (see Deza in References) or Crystal ball sequence for 11-dimensional cubic lattice.
%C A240876 This is row/column 11 of the Delannoy numbers array, A008288, which is the main entry for these numbers, listing many more properties. - _Peter Munn_, Jan 05 2023
%D A240876 E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 230 (paragraph 3.6.6).
%H A240876 Bruno Berselli, <a href="/A240876/b240876.txt">Table of n, a(n) for n = 0..1000</a>
%H A240876 D. Bump, K. Choi, P. Kurlberg, and J. Vaaler, <a href="http://www.cecm.sfu.ca/~choi/paper/lrh.pdf">A local Riemann hypothesis, I</a> pages 16 and 17.
%H A240876 OEIS Wiki, <a href="http://oeis.org/wiki/Centered_orthoplicial_polytopic_numbers#Table_of_sequences">Centered orthoplex numbers</a>, see Table of formulas and values (row 11).
%H A240876 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F A240876 G.f.: (1 + x)^11 / (1 - x)^12.
%F A240876 a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12), with initial values as shown.
%F A240876 a(n) = (2*n + 1)*(2*n*(n + 1)*(n^2 + n + 5)*(2*n^2 + 2*n + 51)*(n^4 + 2*n^3 + 68*n^2 + 67*n + 537)/155925 + 1).
%F A240876 a(n) = A008421(n) + 2*Sum_{i=0..n-1} A008421(i) for n > 0, a(0) = 1.
%F A240876 Sum_{n >= 0} 1/a(n) = 1.047847848425287358769594801715758965260...
%F A240876 a(n) = Sum_{k = 0..min(11,n)} 2^k*binomial(11,k)*binomial(n,k). See Bump et al. - _Tom Copeland_, Sep 05 2014
%t A240876 CoefficientList[Series[(1 + x)^11/(1 - x)^12, {x, 0, 30}], x]
%t A240876 LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{1,23,265,2047,11969,56695,227305,795455,2485825,7059735,18474633,45046719},30] (* _Harvey P. Dale_, Apr 15 2018 *)
%o A240876 (PARI) Vec((1+x)^11/(1-x)^12+O(x^30))
%o A240876 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(),m); Coefficients(R!((1+x)^11/(1-x)^12));
%o A240876 (Maxima) makelist(coeff(taylor((1+x)^11/(1-x)^12, x, 0, n), x, n), n, 0, 30);
%o A240876 (Sage)
%o A240876 m = 30; L.<x> = PowerSeriesRing(ZZ, m)
%o A240876 f = (1+x)^11/(1-x)^12
%o A240876 print(f.coefficients())
%Y A240876 Row/column 11 of A008288.
%Y A240876 Cf. similar sequences with g.f. (1+x)^m/(1-x)^(m+1): A005408 (m=1), A001844 .. A001849 (m=2..7), A008417 (m=8), A008419 (m=9), A008421 (m=10), this sequence (m=11), A053805 (m=12).
%Y A240876 Subsequence of the odd numbers, A005408.
%K A240876 nonn,easy
%O A240876 0,2
%A A240876 _Bruno Berselli_, Apr 16 2014
%E A240876 Edited by _M. F. Hasler_, May 07 2018