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 A001780 #32 Jan 18 2024 09:48:12
%S A001780 1,8,37,128,367,920,2083,4352,8518,15792,27966,47616,78354,125136,
%T A001780 194634,295680,439791,641784,920491,1299584,1808521,2483624,3369301,
%U A001780 4519424,5998876,7885280,10270924,13264896
%N A001780 Expansion of 1/((1+x)(1-x)^9).
%H A001780 Vincenzo Librandi, <a href="/A001780/b001780.txt">Table of n, a(n) for n = 0..2000</a>
%H A001780 Jia Huang, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Huang/huang8.html">Partially Palindromic Compositions</a>, J. Int. Seq. (2023) Vol. 26, Art. 23.4.1. See pp. 4, 17.
%H A001780 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (8,-27,48,-42,0,42,-48,27,-8,1).
%F A001780 a(n) = 431*n/168 + (-1)^n/512 + 391*n^3/288 + 26011*n^2/10080 + 797*n^4/1920 + 11*n^5/144 + n^6/120 + n^7/2016 + n^8/80640 + 511/512. - R. J. Mathar, Mar 15 2011
%F A001780 Boas-Buck recurrence: a(n) = (1/n)*Sum_{p=0..n-1} (9 + (-1)^(n-p))*a(p), n >= 1, a(0) = 1. See the Boas-Buck comment in A046521 (here for the unsigned column k = 4 with offset 0). - _Wolfdieter Lang_, Aug 10 2017
%F A001780 a(n)+a(n+1) = A000581(n+9) . - _R. J. Mathar_, Jan 06 2021
%o A001780 (PARI) Vec(1/(1+x)/(1-x)^9+O(x^99)) \\ _Charles R Greathouse IV_, Apr 18 2012
%Y A001780 Cf. A001769, A158454 (signed column k=4), A001779 (first differences), A169796 (binomial trans.).
%K A001780 nonn,easy
%O A001780 0,2
%A A001780 _N. J. A. Sloane_