A376626 - OEIS

%I #9 Oct 01 2024 05:18:15

%S 1,1,2,2,2,1,3,6,3,3,7,7,6,6,9,13,12,11,16,18,17,20,22,26,28,31,36,36,

%T 42,46,50,57,61,69,72,75,87,97,100,108,126,136,141,151,167,188,195,

%U 207,233,254,265,279,315,339,355,380,417,455,473,503,551,600,627,667,730

%N G.f.: Sum_{k>=0} x^(k*(k+1)/2) * Product_{j=1..k} (1 + x^(2*j-1))^2.

%H Vaclav Kotesovec, <a href="/A376626/b376626.txt">Table of n, a(n) for n = 0..10000</a>

%F G.f.: Sum_{k>=0} Product_{j=1..k} (1 + x^(2*j-1))^2 * x^j.

%F a(n) ~ c * A376659^sqrt(n) / sqrt(n), where c = sqrt(1/14 + sinh(arcsinh(75*sqrt(69)/2)/3)/(7*sqrt(69))) = 0.3792934340515155206194952273079851598271882968396...

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

%t nmax = 100; p = 1; s = 1; Do[p = Expand[p*(1 + x^(2*k - 1))*(1 + x^(2*k - 1))*x^k]; p = Take[p, Min[nmax + 1, Exponent[p, x] + 1, Length[p]]]; s += p;, {k, 1, Sqrt[2*nmax]}]; Take[CoefficientList[s, x], nmax + 1]

%Y Cf. A376580, A376623, A376630, A376659.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Sep 30 2024