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

Author

Paul D. Hanna, Nov 30 2018

Keywords

• nonn

Examples

			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 + ...
		

Links

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

Crossrefs

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

Programs

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),", ") )

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