A316596 - OEIS

%I #9 Jul 10 2018 08:09:27

%S 1,3,10,35,127,462,1716,6440,24310,92378,352737,1352078,5200301,

%T 20058384,77558760,300540195,1166803440,4537567657,17672631900,

%U 68923265697,269128937220,1052049481860,4116715368841,16123801841550,63205303218877,247959266493500,973469712824056,3824345300380385,15033633249846102,59132290782430712,232714176627630544,916312070471589206

%N a(n) equals the coefficient of x^(2*n-1) in Sum_{m>=0} (x^m + 1/x^m)^m for n >= 1.

%C This sequence equals a bisection of A304638; a(n) = A304638(2*n-1) for n >= 1.

%H Paul D. Hanna, <a href="/A316596/b316596.txt">Table of n, a(n) for n = 1..200</a>

%F a(n) ~ 2^(2*n-1) / sqrt(Pi*n). - _Vaclav Kotesovec_, Jul 10 2018

%o (PARI) {a(n) = polcoeff( sum(m=1, 2*n-1, (x^-m + x^m)^m + O(x^(2*n))), 2*n-1, x)}

%o for(n=1, 40, print1(a(n), ", "))

%Y Cf. A304638, A316590, A316591, A316592, A316593, A316594, A316595.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jul 08 2018