A160461 Coefficients in the expansion of C/B^2, in Watson's notation of page 106.

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

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 * A365631 A117487 A263348

Adjacent sequences: A160458 A160459 A160460 * A160462 A160463 A160464

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 13 2009

Status

approved