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 A327770 #37 Aug 11 2025 07:09:29
%S A327770 1,47,2301,112747,5524601,270705447,13264566901,649963778147,
%T A327770 31848225129201,1560563031330847,76467588535211501,
%U A327770 3746911838225363547,183598680073042813801,8996335323579097876247,440820430855375795936101,21600201111913414000868947
%N A327770 a(n) = (23 * 7^(2*n) + 1)/24. Sequence related to the properties of the partition function A000041 modulo a power of 7.
%C A327770 If p(n) = A000041(n) is the partition function, Watson (1938) proved that p(7^(2*m)*n + a(m)) == 0 mod 7^(m+1) for n >= 0 and m >= 1. (Obviously, this is not always true for m = 0).
%C A327770 For m=1 and n=0, p(7^(2*1)*0 + a(1)) = p(47) = 7^(1+1) * 2546.
%C A327770 For m=1 and n=1, p(7^(2*1)*1 + a(1)) = p(96) = 7^(1+1) * 2410496.
%C A327770 For m=1 and n=2, p(7^(2*1)*2 + a(1)) = p(145) = 7^(1+1) * 508344041.
%C A327770 For m=2 and n=0, p(7^(2*2)*0 + a(2)) = p(2301) = 7^(2+1) * 49629361905981812695622866669844910256876089360.
%C A327770 Essentially the same as A052463. - _R. J. Mathar_, Oct 08 2019
%H A327770 Colin Barker, <a href="/A327770/b327770.txt">Table of n, a(n) for n = 0..500</a>
%H A327770 G. N. Watson, <a href="https://gdz.sub.uni-goettingen.de/id/PPN243919689_0179">Ramanujans Vermutung über Zerfällungsanzahlen</a>, J. Reine Angew. Math. (Crelle), 179 (1938), 97-128; see pp. 118 and 124.
%H A327770 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunctionPCongruences.html">Partition Function P Congruences</a>.
%H A327770 Wikipedia, <a href="https://en.wikipedia.org/wiki/G._N._Watson">G. N. Watson</a>.
%H A327770 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (50,-49).
%F A327770 From _Colin Barker_, Sep 25 2019: (Start)
%F A327770 G.f.: (1 - 3*x) / ((1 - x)*(1 - 49*x)).
%F A327770 a(n) = 50*a(n-1) - 49*a(n-2) for n>1.
%F A327770 (End)
%t A327770 CoefficientList[Series[(1 - 3 x)/((1 - x) (1 - 49 x)), {x, 0, 15}], x] (* _Michael De Vlieger_, Sep 27 2019 *)
%t A327770 LinearRecurrence[{50,-49},{1,47},20] (* _Harvey P. Dale_, Mar 09 2023 *)
%o A327770 (PARI) a(n) = (23 * 7^(2*n) + 1)/24; \\ _Michel Marcus_, Sep 25 2019
%o A327770 (PARI) Vec((1 - 3*x) / ((1 - x)*(1 - 49*x)) + O(x^20)) \\ _Colin Barker_, Sep 25 2019
%Y A327770 Cf. A052463, A071746, A213261, A327714, A327582.
%K A327770 nonn,easy
%O A327770 0,2
%A A327770 _Petros Hadjicostas_, Sep 24 2019