A322201 Main diagonal of square table A322200.

0, 2, 10, 26, 90, 262, 994, 3446, 13050, 48698, 185310, 705454, 2706354, 10400626, 40123534, 155118406, 601106490, 2333606254, 9075235522, 35345263838, 137846899790, 538257884918, 2104100374694, 8233430727646, 32247609134418, 126410606439062, 495918553749434, 1946939425794206, 7648690681007998, 30067266499541098, 118264581875657214, 465428353255261150

Offset

0,2

Links

Paul D. Hanna, Table of n, a(n) for n = 0..400

Formula

a(n) = coefficient of x^n*y^n/(2*n) in Sum_{n>=1} -log(1 - (x^n + y^n)) for n>=0.

a(n) ~ 4^n / sqrt(Pi*n). - Vaclav Kotesovec, Jun 18 2019

Example

L.g.f.: L(x) = 2*x + 10*x^2/2 + 26*x^3/3 + 90*x^4/4 + 262*x^5/5 + 994*x^6/6 + 3446*x^7/7 + 13050*x^8/8 + 48698*x^9/9 + 185310*x^10/10 + 705454*x^11/11 + 2706354*x^12/12 + ...
such that
exp( L(x) ) = 1 + 2*x + 7*x^2 + 20*x^3 + 63*x^4 + 190*x^5 + 613*x^6 + 1976*x^7 + 6604*x^8 + 22368*x^9 + 77270*x^10 + 270208*x^11 + 956780*x^12 + ...

Prog

(PARI)
{L = sum(n=1, 61, -log(1 - (x^n + y^n) +O(x^61) +O(y^61)) ); }
{a(n) = polcoeff( 2*n*polcoeff( L, n, x), n, y)}
for(n=0, 35, print1( a(n), ", ") )

Crossrefs

Cf. A322200, A322202, A322203, A322205, A322207, A322209.

Sequence in context: A025589 A084182 A321240 * A099583 A328743 A133479

Adjacent sequences: A322198 A322199 A322200 * A322202 A322203 A322204

Keyword

nonn

Author

Paul D. Hanna, Nov 30 2018

Status

approved