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 A097299 #11 May 02 2025 10:31:54 %S A097299 6,49,225,765,2145,5247,11583,23595,45045,81510,140998,234702,377910, %T A097299 591090,901170,1343034,1961256,2812095,3965775,5509075,7548255, %U A097299 10212345,13656825,18067725,23666175,30713436,39516444,50433900,63882940 %N A097299 Ninth column (m=8) of (1,6)-Pascal triangle A096956. %H A097299 Paolo Xausa, <a href="/A097299/b097299.txt">Table of n, a(n) for n = 0..10000</a> %H A097299 <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 A097299 a(n) = A096956(n+8, 8) = 6*b(n) - 5*b(n-1) = (n+48)*binomial(n+7, 7)/8, with b(n) = A000581(n+8) = binomial(n+8, 8). %F A097299 G.f.: (6-5*x)/(1-x)^9. %t A097299 A097299[n_] := (n + 48)*Binomial[n + 7, 7]/8; %t A097299 Array[A097299, 50, 0] (* _Paolo Xausa_, May 02 2025 *) %Y A097299 Cf. A000581, A096956. %Y A097299 Cf. other columns: A096957 (m = 3), A096958 (m = 4), A096959 (m = 5), A097297 (m = 6), A097298 (m = 7), A097300 (m = 9). %K A097299 nonn,easy %O A097299 0,1 %A A097299 _Wolfdieter Lang_, Aug 13 2004