A160534 Coefficients in the expansion of B^7/C, in Watson's notation of page 118.

1, -7, 14, 7, -49, 21, 35, 42, -56, -119, 105, -70, 147, 147, -133, -168, -231, 252, -154, 315, 441, 7, -644, -574, 595, -679, 735, 574, 196, -406, -840, 840, -1470, 854, 1260, 21, -1617, -966, 1575, -1176, 1785, 1470, 35, -1974, -2058, 1533, -1988, 1932, 2387, -301, -2170, -2016, 3087, -2422

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Watson, G. N., Ramanujans Vermutung ueber Zerfaellungsanzahlen. J. Reine Angew. Math. (Crelle), 179 (1938), 97-128.

Formula

See Maple code in A160525 for formula.

Euler transform of period 7 sequence [ -7, -7, -7, -7, -7, -7, -6, ...]. - Alois P. Heinz, Jan 07 2017

Example

1-7*x^24+14*x^48+7*x^72-49*x^96+21*x^120+35*x^144+42*x^168-...

Maple

with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
      `if`(irem(d, 7)=0, -6, -7), d=divisors(j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..70);  # Alois P. Heinz, Jan 07 2017

Mathematica

a[n_] := a[n] = If[n==0, 1, Sum[DivisorSum[j, #*If[Mod[#, 7]==0, -6, -7]&]* a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 0, 70}] (* Jean-François Alcover, Mar 13 2017, after Alois P. Heinz *)

Crossrefs

Sequence in context: A340312 A029844 A000730 * A022699 A362586 A102654

Adjacent sequences: A160531 A160532 A160533 * A160535 A160536 A160537

Keyword

sign

Author

N. J. A. Sloane, Nov 14 2009

Status

approved