A282919 a(n) = A000041(49*n + 47).

124754, 118114304, 24908858009, 2366022741845, 133978259344888, 5234371069753672, 154043597379576030, 3617712763867604423, 70593393646562135510, 1178875491155735802646, 17229817230617210720599, 224282898599046831034631, 2636785814481962651219075

Offset: 0

Author

Seiichi Manyama, Feb 24 2017

Keywords

• nonn

References

• G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012, See p. 179.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A160528, A282920, A282921, A282922, A282923, A282924, A282925, A282926, A282927, A282928, A282929, A282930, A282931, A282932.

Cf. A000041, A213261 (p(7*n + 5)), A277958, A278559 (p(25*n + 24)), this sequence (p(49*n + 47)).

Programs

Mathematica

Table[PartitionsP[49n+47],{n,0,12}] (* Indranil Ghosh, Feb 25 2017 *)

PARI

a(n) = numbpart(49*n+47); \\ Indranil Ghosh, Feb 25 2017

Formula

a(n) = A213261(7*n + 6) = A000041(49*n + 47).

a(n) = 2546 * 7^2 * A160528(n) + 48934 * 7^4 * A282920(n-1) + 1418989 * 7^5 * A282921(n-2) + 2488800 * 7^7 * A282922(n-3) + 2394438 * 7^9 * A282923(n-4) + 1437047 * 7^11 * A282924(n-5) + 4043313 * 7^12 * A282925(n-6) + 161744 * 7^15 * A282926(n-7) + 32136 * 7^17 * A282927(n-8) + 31734 * 7^18 * A282928(n-9) + 3120 * 7^20 * A282929(n-10) + 204 * 7^22 * A282930(n-11) + 8 * 7^24 * A282931(n-12) + 7^25 * A282932(n-13) for n >= 13.