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 A090394 #17 Feb 23 2025 20:13:04
%S A090394 0,40320,95616,170856,272584,409360,592296,835702,1157857,1581921,
%T A090394 2137005,2859417,3794103,4996303,6533443,8487285,10956358,14058694,
%U A090394 17934894,22751550,28705050,36025794,44982850,55889080,69106767
%N A090394 Ninth diagonal (m=8) of triangle A084938; a(n) = A084938(n+8,n) = (n^8 + 84*n^7 + 3346*n^6 + 84840*n^5 + 1550689*n^4 + 21632436*n^3 + 224782284*n^2 + 1377648720*n)/40320.
%H A090394 Chai Wah Wu, <a href="/A090394/b090394.txt">Table of n, a(n) for n = 0..1000</a>
%H A090394 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).
%F A090394 a(n) = A084938(n+8, n) = Sum_{k=0..8} A090238(8, k)*binomial(n, k).
%F A090394 From _Chai Wah Wu_, Jun 04 2016: (Start)
%F A090394 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n > 8.
%F A090394 G.f.: x*(29093*x^7 - 212062*x^6 + 663528*x^5 - 1155496*x^4 + 1209824*x^3 - 761832*x^2 + 267264*x - 40320)/(x - 1)^9. (End)
%t A090394 LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,40320,95616,170856,272584,409360,592296,835702,1157857},30] (* _Harvey P. Dale_, Apr 04 2017 *)
%o A090394 (Python)
%o A090394 from itertools import islice
%o A090394 def A090394_generator():
%o A090394 m = [1, 7, 33, 135, 531, 2109, 8411, 29093, 0]
%o A090394 yield m[-1]
%o A090394 while True:
%o A090394 for i in range(8):
%o A090394 m[i+1]+= m[i]
%o A090394 yield m[-1]
%o A090394 list(islice(A090394_generator(),0,50,1)) # _Chai Wah Wu_, Nov 14 2014
%Y A090394 Cf. A084938 A090238.
%K A090394 easy,nonn
%O A090394 0,2
%A A090394 _Philippe Deléham_, Jan 31 2004