A327771 a(n) = p(49*n + 47)/49, where p(k) denotes the k-th partition number (i.e., A000041).

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

Table of n, a(n) for n=0..13.

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

Crossrefs

Cf. A000041, A052462, A052463, A052465, A052466, A071746, A213261, A327714, A327582, A327770.

Sequence in context: A135924 A250686 A307473 * A035876 A072435 A050413

Adjacent sequences: A327768 A327769 A327770 * A327772 A327773 A327774

Keyword

nonn

Author

Petros Hadjicostas, Sep 24 2019

Status

approved