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 A327771 #26 Aug 11 2025 05:11:51
%S A327771 2546,2410496,508344041,48286178405,2734250190712,106823899382728,
%T A327771 3143746885297470,73830872731991927,1440681502991063990,
%U A327771 24058683492974200054,351628923073820626951,4577202012225445531319,53811955397591074514675,577896157936323089053580
%N A327771 a(n) = p(49*n + 47)/49, where p(k) denotes the k-th partition number (i.e., A000041).
%C A327771 Watson (1938), p. 120, proved that p(7*n + 5) == 0 (mod 7) and p(49*n + 47) == 0 (mod 49) for n >= 0, where p() = A000041(). For more general congruence results modulo a power of 7 by George Neville Watson regarding the partition function, see A327582 and A327770.
%H A327771 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 p. 120.
%H A327771 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunctionPCongruences.html">Partition Function P Congruences</a>.
%H A327771 Wikipedia, <a href="https://en.wikipedia.org/wiki/G._N._Watson">G. N. Watson</a>.
%F A327771 a(n) = A000041(49*n + 47)/49.
%t A327771 Table[PartitionsP[49n+47]/49,{n, 0, 13}] (* _Metin Sariyar_, Sep 25 2019 *)
%o A327771 (PARI) a(n) = numbpart(49*n + 47)/49; \\ _Michel Marcus_, Sep 25 2019
%Y A327771 Cf. A000041, A052462, A052463, A052465, A052466, A071746, A213261, A327714, A327582, A327770.
%K A327771 nonn
%O A327771 0,1
%A A327771 _Petros Hadjicostas_, Sep 24 2019