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A327771
a(n) = p(49*n + 47)/49, where p(k) denotes the k-th partition number (i.e., A000041).
0
2546, 2410496, 508344041, 48286178405, 2734250190712, 106823899382728, 3143746885297470, 73830872731991927, 1440681502991063990, 24058683492974200054, 351628923073820626951, 4577202012225445531319, 53811955397591074514675, 577896157936323089053580
OFFSET
0,1
COMMENTS
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.
LINKS
G. N. Watson, Ramanujans Vermutung über Zerfällungsanzahlen, J. Reine Angew. Math. (Crelle), 179 (1938), 97-128; see p. 120.
Eric Weisstein's World of Mathematics, Partition Function P Congruences.
Wikipedia, G. N. Watson.
FORMULA
a(n) = A000041(49*n + 47)/49.
MATHEMATICA
Table[PartitionsP[49n+47]/49, {n, 0, 13}] (* Metin Sariyar, Sep 25 2019 *)
PROG
(PARI) a(n) = numbpart(49*n + 47)/49; \\ Michel Marcus, Sep 25 2019
KEYWORD
nonn
AUTHOR
Petros Hadjicostas, Sep 24 2019
STATUS
approved