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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 (list; graph; refs; listen; history; text; internal format)
 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 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). Cf. A000041, A015128, A278690, A298311. Sequence in context: A325649 A325719 A000710 * A117487 A263348 A328548 Adjacent sequences:  A160458 A160459 A160460 * A160462 A160463 A160464 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Nov 13 2009 STATUS approved

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Last modified August 1 22:36 EDT 2021. Contains 346408 sequences. (Running on oeis4.)