A316596 a(n) equals the coefficient of x^(2*n-1) in Sum_{m>=0} (x^m + 1/x^m)^m for n >= 1.

1, 3, 10, 35, 127, 462, 1716, 6440, 24310, 92378, 352737, 1352078, 5200301, 20058384, 77558760, 300540195, 1166803440, 4537567657, 17672631900, 68923265697, 269128937220, 1052049481860, 4116715368841, 16123801841550, 63205303218877, 247959266493500, 973469712824056, 3824345300380385, 15033633249846102, 59132290782430712, 232714176627630544, 916312070471589206

Offset

1,2

Comments

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

Links

Paul D. Hanna, Table of n, a(n) for n = 1..200

Formula

a(n) ~ 2^(2*n-1) / sqrt(Pi*n). - Vaclav Kotesovec, Jul 10 2018

Prog

(PARI) {a(n) = polcoeff( sum(m=1, 2*n-1, (x^-m + x^m)^m + O(x^(2*n))), 2*n-1, x)}
for(n=1, 40, print1(a(n), ", "))

Crossrefs

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

Sequence in context: A072266 A085282 A149036 * A047127 A114196 A346739

Adjacent sequences: A316593 A316594 A316595 * A316597 A316598 A316599

Keyword

nonn

Author

Paul D. Hanna, Jul 08 2018

Status

approved