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A273228 G.f. is the fourth power of the g.f. of A006950.

%I A273228 #25 Mar 19 2025 13:21:14
%S A273228 1,4,10,24,55,116,230,440,819,1480,2602,4480,7580,12604,20620,33272,
%T A273228 53029,83520,130088,200600,306488,464168,697150,1039032,1537435,
%U A273228 2259300,3298428,4785880,6903657,9903040,14129846,20058488,28336790,39845456,55778050,77747328,107924347,149221160
%N A273228 G.f. is the fourth power of the g.f. of A006950.
%C A273228 Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).
%H A273228 G. C. Greubel, <a href="/A273228/b273228.txt">Table of n, a(n) for n = 0..1000</a>
%H A273228 M. D. Hirschhorn and J. A. Sellers, <a href="http://dx.doi.org/10.1007/s11139-010-9225-6">Arithmetic properties of partitions with odd parts distinct</a>, Ramanujan J. 22 (2010), 273--284.
%H A273228 M. S. Mahadeva Naika and D. S. Gireesh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL19/Naika/naika2.html">Arithmetic Properties of Partition k-tuples with Odd Parts Distinct</a>, JIS, Vol. 19 (2016), Article 16.5.7
%H A273228 L. Wang, <a href="http://dx.doi.org/10.1142/S1793042115500773">Arithmetic properties of partition triples with odd parts distinct</a>, Int. J. Number Theory, 11 (2015), 1791--1805.
%H A273228 L. Wang, <a href="http://dx.doi.org/10.1017/S0004972715000647">Arithmetic properties of partition quadruples with odd parts distinct</a>, Bull. Aust. Math. Soc., doi:10.1017/S0004972715000647.
%H A273228 L. Wang, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Wang2/wang31.html">New congruences for partitions where the odd parts are distinct</a>, J. Integer Seq. (2015), article 15.4.2.
%F A273228 G.f.: Product_{k>=1} (1 + x^k)^4 / (1 - x^(4*k))^4, corrected by _Vaclav Kotesovec_, Mar 25 2017
%F A273228 Expansion of 1 / psi(-x)^4 in powers of x where psi() is a Ramanujan theta function.
%F A273228 a(n) ~ exp(sqrt(2*n)*Pi) / (2^(9/4)*n^(7/4)). - _Vaclav Kotesovec_, Mar 25 2017
%p A273228 Digits:=200:with(PolynomialTools): with(qseries): with(ListTools):
%p A273228 GenFun:=series(etaq(q,2,1000)^4/etaq(q,1,1000)^4/etaq(q,4,1000)^4,q,50):
%p A273228 CoefficientList(sort(convert(GenFun,polynom),q,ascending),q);
%t A273228 nmax = 30; CoefficientList[Series[Product[(1 + x^k)^4 / (1 - x^(4*k))^4, {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Mar 25 2017 *)
%t A273228 CoefficientList[Series[1/(QPochhammer[q, -q]*QPochhammer[q^2, q^2])^4, {q, 0, 50}], q] (* _G. C. Greubel_, Apr 17 2018 *)
%Y A273228 Cf. A006960, A273226.
%K A273228 nonn
%O A273228 0,2
%A A273228 _M.S. Mahadeva Naika_, May 18 2016
%E A273228 Edited by _N. J. A. Sloane_, May 26 2016