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A160461
Coefficients in the expansion of C/B^2, in Watson's notation of page 106.
13
1, 2, 5, 10, 20, 35, 63, 105, 175, 280, 444, 685, 1050, 1575, 2345, 3439, 5005, 7195, 10275, 14525, 20405, 28428, 39375, 54150, 74080, 100715, 136265, 183365, 245645, 327485, 434810, 574790, 756965, 992950, 1297940, 1690500, 2194642, 2839695, 3663225, 4711160
OFFSET
0,2
LINKS
G. N. Watson, Ramanujans Vermutung über Zerfällungsanzahlen, J. Reine Angew. Math. (Crelle), 179 (1938), 97-128.
FORMULA
See Maple code in A160458 for formula.
a(n) ~ sqrt(3)*exp(sqrt(6*n/5)*Pi)/(20*n). - Vaclav Kotesovec, Nov 26 2016
G.f.: 1/Product_{n >= 1} ( 1 - x^(n/gcd(n,k)) ) for k = 5. Cf. A000041 (k = 1), A015128 (k = 2), A278690 (k = 3) and A298311 (k = 4). - Peter Bala, Nov 17 2020
EXAMPLE
x^3+2*x^27+5*x^51+10*x^75+20*x^99+35*x^123+63*x^147+...
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1 - x^(5*k))/(1 - x^k)^2, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Nov 26 2016 *)
CROSSREFS
Cf. Product_{n>=1} (1 - x^(5*n))^k/(1 - x^n)^(k + 1): this sequence (k=1), A160462 (k=2), A160463 (k=3), A160506 (k=4), A071734 (k=5), A160460 (k=6), A160521 (k=7), A278555 (k=12), A278556 (k=18), A278557 (k=24), A278558 (k=30).
Sequence in context: A325719 A000710 A384998 * A365631 A117487 A263348
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 13 2009
STATUS
approved