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 A346797 #21 Aug 05 2021 16:25:00
%S A346797 1,0,1,0,1,1,1,2,1,3,2,3,4,3,7,4,9,6,10,11,11,17,13,22,19,25,29,28,42,
%T A346797 34,53,46,61,67,69,92,83,115,109,133,149,152,198,182,243,233,282,309,
%U A346797 324,398,385,485,483,563,621,648,784,768,944,947,1096,1194,1262
%N A346797 Number of partitions of n into parts congruent to 0, 2 or 5 (mod 7).
%H A346797 Ludovic Schwob, <a href="/A346797/b346797.txt">Table of n, a(n) for n = 0..10000</a>
%F A346797 G.f.: Product_{k>=1} 1/((1 - x^(7*k))*(1 - x^(7*k-2))*(1 - x^(7*k-5))).
%F A346797 a(n) = a(n-2) + a(n-5) - a(n-11) - a(n-17) + + - - (with a(0)=1 and a(n) = 0 for negative n), where 2, 5, 11, 17, ... is the sequence A274830.
%F A346797 a(n) ~ exp(Pi*sqrt(2*n/7)) / (8*cos(3*Pi/14)*n). - _Vaclav Kotesovec_, Aug 05 2021
%e A346797 For n=17 the a(17)=6 solutions are 2+2+2+2+2+2+5, 2+2+2+2+2+7, 2+2+2+2+9, 2+5+5+5, 5+5+7 and 5+12.
%t A346797 CoefficientList[Series[Product[1/((1 - x^(7*k))(1 - x^(7*k-2))(1 - x^(7*k-5))),{k,52}],{x,0,52}],x] (* _Stefano Spezia_, Aug 04 2021 *)
%Y A346797 Cf. A000041, A047386, A274830, A006950, A036820, A036822, A195848, A035363, A195849, A346798.
%K A346797 nonn
%O A346797 0,8
%A A346797 _Ludovic Schwob_, Aug 04 2021