login
A273226
G.f. is the cube of the g.f. of A006950.
4
1, 3, 6, 13, 27, 51, 91, 159, 273, 455, 738, 1179, 1860, 2886, 4410, 6667, 9981, 14781, 21671, 31512, 45474, 65113, 92547, 130689, 183439, 255930, 355017, 489895, 672672, 919152, 1250107, 1692846, 2282895, 3066180, 4102224, 5468160, 7263217, 9614436, 12684633, 16682276
OFFSET
0,2
LINKS
M. D. Hirschhorn and J. A. Sellers, Arithmetic properties of partitions with odd parts distinct, Ramanujan J. 22 (2010), 273--284.
L. Wang, Arithmetic properties of partition triples with odd parts distinct, Int. J. Number Theory, 11 (2015), 1791--1805.
L. Wang, Arithmetic properties of partition quadruples with odd parts distinct, Bull. Aust. Math. Soc., doi:10.1017/S0004972715000647.
L. Wang, New congruences for partitions where the odd parts are distinct, J. Integer Seq. (2015), article 15.4.2.
FORMULA
G.f.: Product_{k>=1} (1 + x^k)^3 / (1 - x^(4*k))^3, corrected by Vaclav Kotesovec, Mar 25 2017.
a(n) ~ 3*exp(sqrt(3*n/2)*Pi) / (16*n^(3/2)). - Vaclav Kotesovec, Mar 25 2017
MAPLE
N:= 50:
G:= mul((1+x^k)^3, k=1..N)/mul((1-x^(4*k))^3, k=1..N/4):
S:= series(G, x, N+1):
seq(coeff(S, x, j), j=0..N); # Robert Israel, Jan 21 2019
MATHEMATICA
s = QPochhammer[-1, x]^3/(8*QPochhammer[x^4, x^4]^3) + O[x]^40; CoefficientList[s, x] (* Jean-François Alcover, May 20 2016 *)
CROSSREFS
Cf. A006950.
Sequence in context: A215989 A215980 A215979 * A291726 A280563 A281283
KEYWORD
nonn
AUTHOR
M.S. Mahadeva Naika, May 18 2016
EXTENSIONS
Edited by N. J. A. Sloane, May 26 2016
STATUS
approved