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%I #23 Sep 26 2019 01:56:00
%S 2546,2410496,508344041,48286178405,2734250190712,106823899382728,
%T 3143746885297470,73830872731991927,1440681502991063990,
%U 24058683492974200054,351628923073820626951,4577202012225445531319,53811955397591074514675,577896157936323089053580
%N a(n) = p(49*n + 47)/49, where p(k) denotes the k-th partition number (i.e., A000041).
%C 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 G. N. Watson, <a href="http://www.digizeitschriften.de/dms/resolveppn/?PID=GDZPPN002174499">Ramanujans Vermutung über Zerfällungsanzahlen</a>, J. Reine Angew. Math. (Crelle), 179 (1938), 97-128; see p. 120.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PartitionFunctionPCongruences.html">Partition Function P Congruences</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/G._N._Watson">G. N. Watson</a>.
%F a(n) = A000041(49*n + 47)/49.
%t Table[PartitionsP[49n+47]/49,{n, 0, 13}] (* _Metin Sariyar_, Sep 25 2019 *)
%o (PARI) a(n) = numbpart(49*n + 47)/49; \\ _Michel Marcus_, Sep 25 2019
%Y Cf. A000041, A052462, A052463, A052465, A052466, A071746, A213261, A327714, A327582, A327770.
%K nonn
%O 0,1
%A _Petros Hadjicostas_, Sep 24 2019
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