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A322201 Main diagonal of square table A322200. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 11 08:50 EDT 2020. Contains 335626 sequences. (Running on oeis4.)