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 A264894 #22 Feb 16 2025 08:33:27
%S A264894 0,1,261,1956,7291,19500,42846,82621,145146,237771,368875,547866,
%T A264894 785181,1092286,1481676,1966875,2562436,3283941,4148001,5172256,
%U A264894 6375375,7777056,9398026,11260041,13385886,15799375,18525351,21589686,25019281,28842066,33087000
%N A264894 a(n) = n*(7*n - 5)*(49*n^2 - 35*n - 10)/8.
%C A264894 Doubly 9-gonal (or nonagonal) numbers.
%H A264894 G. C. Greubel, <a href="/A264894/b264894.txt">Table of n, a(n) for n = 0..5000</a>
%H A264894 OEIS Wiki, <a href="https://oeis.org/wiki/Figurate_numbers">Figurate numbers</a>
%H A264894 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/NonagonalNumber.html">Nonagonal Number</a>
%H A264894 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1)
%F A264894 G.f.: x*(1 + 256*x + 661*x^2 + 111*x^3)/(1 - x)^5.
%F A264894 a(n) = A001106(A001106(n)).
%F A264894 Sum_{n>0} 1/a(n) = (4*(sqrt(65)*gamma + sqrt(65)*polygamma(0, 2/7) - 5*polygamma(0, (1/14)*(9 - sqrt(65))) + 5*polygamma(0, (1/14)*(9 + sqrt(65)))))/(25*sqrt(65)) = 1.0045877861645573..., where gamma is the Euler-Mascheroni constant (A001620), and polygamma is the derivative of the logarithm of the gamma function.
%t A264894 Table[n (7 n - 5) (49 n^2 - 35 n - 10)/8, {n, 0, 30}]
%t A264894 LinearRecurrence[{5,-10,10,-5,1},{0,1,261,1956,7291},40] (* _Harvey P. Dale_, Apr 29 2017 *)
%o A264894 (PARI) vector(100, n, n--; n*(7*n-5)*(49*n^2-35*n-10)/8) \\ _Altug Alkan_, Nov 27 2015
%o A264894 (Magma) [n*(7*n-5)*(49*n^2-35*n-10)/8: n in [0..30]]; // _Vincenzo Librandi_, Nov 28 2015
%Y A264894 Cf. A001106, A002817, A000583, A232713, A063249.
%K A264894 nonn,easy
%O A264894 0,3
%A A264894 _Ilya Gutkovskiy_, Nov 27 2015