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 A306752 #20 Jun 21 2021 03:01:20 %S A306752 1,1,1,1,1,1,1,1,1,2,10,46,166,496,1288,3004,6436,12871,24312,43776, %T A306752 75736,126940,208336,340120,564928,980629,1817047,3605252,7531836, %U A306752 16146326,34716826,73737316,153430156,311652271,617594122,1195477615,2266064352,4221317464 %N A306752 a(n) = Sum_{k=0..n} binomial(k, 8*(n-k)). %H A306752 Seiichi Manyama, <a href="/A306752/b306752.txt">Table of n, a(n) for n = 0..3528</a> %H A306752 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1,1). %F A306752 G.f.: (1-x)^7/((1-x)^8 - x^9). %F A306752 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) + a(n-9) for n > 8. %F A306752 a(n) = A017867(8*n). %t A306752 a[n_] := Sum[Binomial[k, 8*(n-k)], {k, 0, n}]; Array[a, 38, 0] (* _Amiram Eldar_, Jun 21 2021 *) %o A306752 (PARI) {a(n) = sum(k=0, n, binomial(k, 8*(n-k)))} %o A306752 (PARI) N=66; x='x+O('x^N); Vec((1-x)^7/((1-x)^8-x^9)) %Y A306752 Column 8 of A306680. %Y A306752 Cf. A017867. %K A306752 nonn %O A306752 0,10 %A A306752 _Seiichi Manyama_, Mar 07 2019