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 A097300 #10 May 02 2025 10:31:57 %S A097300 6,55,280,1045,3190,8437,20020,43615,88660,170170,311168,545870, %T A097300 923780,1514870,2416040,3759074,5720330,8532425,12498200,18007275, %U A097300 25555530,35767875,49424700,67492425,91158600,121872036,161388480,211822380 %N A097300 Tenth column (m=9) of (1,6)-Pascal triangle A096956. %H A097300 Paolo Xausa, <a href="/A097300/b097300.txt">Table of n, a(n) for n = 0..10000</a> %H A097300 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1). %F A097300 a(n) = A096956(n+9, 9) = 6*b(n) - 5*b(n-1) = (n+54)*binomial(n+8, 8)/9, with b(n) = A000582(n+9) = binomial(n+9, 9). %F A097300 G.f.: (6-5*x)/(1-x)^10. %t A097300 A097300[n_] := (n + 54)*Binomial[n + 8, 8]/9; %t A097300 Array[A097300, 50, 0] (* _Paolo Xausa_, May 02 2025 *) %Y A097300 Cf. A000582, A096956. %Y A097300 Cf. other columns: A096957 (m = 3), A096958 (m = 4), A096959 (m = 5), A097297 (m = 6), A097298 (m = 7), A097299 (m = 8). %K A097300 nonn,easy %O A097300 0,1 %A A097300 _Wolfdieter Lang_, Aug 13 2004