A160461 - OEIS

%I #14 Nov 17 2020 11:03:41

%S 1,2,5,10,20,35,63,105,175,280,444,685,1050,1575,2345,3439,5005,7195,

%T 10275,14525,20405,28428,39375,54150,74080,100715,136265,183365,

%U 245645,327485,434810,574790,756965,992950,1297940,1690500,2194642,2839695,3663225,4711160

%N Coefficients in the expansion of C/B^2, in Watson's notation of page 106.

%H Seiichi Manyama, <a href="/A160461/b160461.txt">Table of n, a(n) for n = 0..1000</a>

%H Watson, G. N., <a href="http://www.digizeitschriften.de/dms/resolveppn/?PID=GDZPPN002174499">Ramanujans Vermutung ueber Zerfaellungsanzahlen.</a> J. Reine Angew. Math. (Crelle), 179 (1938), 97-128.

%F See Maple code in A160458 for formula.

%F a(n) ~ sqrt(3)*exp(sqrt(6*n/5)*Pi)/(20*n). - _Vaclav Kotesovec_, Nov 26 2016

%F 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

%e x^3+2*x^27+5*x^51+10*x^75+20*x^99+35*x^123+63*x^147+...

%t 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 *)

%Y 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).

%Y Cf. A000041, A015128, A278690, A298311.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 13 2009