%I #13 Jun 12 2019 11:31:01

%S 1,2,4,6,9,14,20,28,40,54,72,98,129,168,220,282,360,460,580,728,912,

%T 1134,1404,1734,2129,2604,3180,3864,4680,5658,6812,8182,9808,11718,

%U 13968,16618,19720,23350,27600,32550,38313

%N Coefficients of the second order mock theta function B(q).

%H Vaclav Kotesovec, <a href="/A153140/b153140.txt">Table of n, a(n) for n = 0..10000</a>

%H R. J. McIntosh, <a href="http://dx.doi.org/10.4153/CMB-2007-028-9">Second order mock theta functions</a>, Canad. Math. Bull. 50 (2007), 284-290.

%F G.f.: Sum_{n >= 0} q^(n^2+n)(1+q^2)(1+q^4)...(1+q^(2n))/(1-q)^2(1-q^3)^2...(1-q^(2n+1))^2.

%F G.f.: Sum_{n >= 0} q^n(1+q)(1+q^3)...(1+q^(2n-1))/(1-q)(1-q^3)...(1-q^(2n+1)).

%F a(n) ~ exp(Pi*sqrt(n/2)) / (2^(5/2) * sqrt(n)). - _Vaclav Kotesovec_, Jun 12 2019

%t nmax = 100; CoefficientList[Series[Sum[x^(k^2+k) * Product[(1+x^(2*j))/(1-x^(2*j+1))^2, {j, 0, k}], {k, 0, Floor[Sqrt[nmax]]}]/2, {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 12 2019 *)

%o (PARI) lista(nn) = my(q = qq + O(qq^nn)); gf = sum(n = 0, nn, q^n * prod(k = 1, n, 1 + q^(2*k-1)) / prod(k = 0, n, 1 - q^(2*k+1))); Vec(gf) \\ _Michel Marcus_, Jun 18 2013

%Y Other '2nd order' mock theta functions are at A006304, A006306.

%K nonn

%O 0,2

%A _Jeremy Lovejoy_, Dec 19 2008

%E More terms from _Michel Marcus_, Jun 18 2013