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A160525
Coefficients in the expansion of C/B^2, in Watson's notation of page 118.
7
1, 2, 5, 10, 20, 36, 65, 109, 183, 295, 471, 732, 1129, 1705, 2554, 3769, 5517, 7979, 11458, 16289, 23007, 32227, 44869, 62028, 85284, 116530, 158432, 214228, 288348, 386224, 515156, 684109, 904963, 1192353, 1565383, 2047642, 2669591, 3468797, 4493351, 5802533
OFFSET
0,2
LINKS
G. N. Watson, Ramanujans Vermutung über Zerfällungsanzahlen, J. Reine Angew. Math. (Crelle), 179 (1938), 97-128.
FORMULA
See Maple code for formula.
G.f.: Product_{n>=1} (1 - x^(7*n))/(1 - x^n)^2. - Seiichi Manyama, Nov 06 2016
a(n) ~ sqrt(13/3) * exp(sqrt(26*n/21)*Pi) / (28*n). - Vaclav Kotesovec, Apr 13 2017
EXAMPLE
G.f. = 1 + 2*x + 5*x^2 + 10*x^3 + 20*x^4 + 36*x^5 + 65*x^6 + 109*x^7 + ...
G.f. = q^5 + 2*q^29 + 5*q^53 + 10*q^77 + 20*q^101 + 36*q^125 + 65*q^149 + 109*q^173 + ...
MAPLE
M1:=1200:
fm:=mul(1-x^n, n=1..M1):
A:=x^(1/7)*subs(x=x^(24/7), fm):
B:=x*subs(x=x^24, fm):
C:=x^7*subs(x=x^168, fm):
t1:=C/B^2;
t2:=series(t1, x, M1);
t3:=subs(x=y^(1/24), t2/x^5);
t4:=series(t3, y, M1/24);
t5:=seriestolist(t4); # A160525
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1 - x^(7*k))/(1 - x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Apr 13 2017 *)
CROSSREFS
Cf. Product_{n>=1} (1 - x^(k*n))/(1 - x^n)^2: A000041 (k=1), A015128 (k=2), A278690 (k=3), A160461 (k=5), this sequence (k=7).
Sequence in context: A103924 A160647 A103925 * A103926 A103927 A103928
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 13 2009
STATUS
approved