A397094 - OEIS

%I #8 Jun 16 2026 11:55:41

%S 1,1,7,33,331,1255,7331,23137,528627,1678091,9634009,28382599,

%T 330241631,950294211,5450472475,15571967713,701569265347,

%U 1972778241139,11081264027421,30752846697963,341394914833541,942115702568569,5177065777113957,14160495993439431,309192824835902071

%N Numerators of coefficients in expansion of Product_{k>=1} (1+x^k)^(k/2).

%C G.f. of a(n)/A046161(n) is the square root of the g.f. for A026007.

%F a(n) / A046161(n) ~ zeta(3)^(1/6) * exp(3^(4/3) * zeta(3)^(1/3) * n^(2/3) / 2^(5/3)) / (2^(7/8) * 3^(1/3) * sqrt(Pi) * n^(2/3)).

%e 1, 1/2, 7/8, 33/16, 331/128, 1255/256, 7331/1024, 23137/2048, 528627/32768, 1678091/65536, ...

%t nmax = 25; CoefficientList[Series[Product[(1+x^k)^(k/2), {k, 1, nmax}], {x, 0, nmax}], x] // Numerator

%Y Denominators are A046161.

%Y Cf. A026007, A232976.

%K nonn,frac

%O 0,3

%A _Vaclav Kotesovec_, Jun 16 2026