A322203 - OEIS

A322203

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

1, 5, 13, 45, 131, 497, 1723, 6525, 24349, 92655, 352727, 1353177, 5200313, 20061767, 77559203, 300553245, 1166803127, 4537617761, 17672631919, 68923449895, 269128942459, 1052050187347, 4116715363823, 16123804567209, 63205303219531, 247959276874717, 973469712897103, 3824345340503999, 15033633249770549, 59132290937828607, 232714176627630575, 916312071072401757

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OFFSET

1,2

LINKS

Paul D. Hanna, Table of n, a(n) for n = 1..400

FORMULA

a(n) = A322200(n,n)/2 for n >= 1.

a(n) ~ 2^(2*n-1) / sqrt(Pi*n). - Vaclav Kotesovec, Jun 18 2019

EXAMPLE

G.f.: L(x) = x + 5*x^2/2 + 13*x^3/3 + 45*x^4/4 + 131*x^5/5 + 497*x^6/6 + 1723*x^7/7 + 6525*x^8/8 + 24349*x^9/9 + 92655*x^10/10 + 352727*x^11/11 + 1353177*x^12/12 + ...

such that

exp( L(x) ) = 1 + x + 3*x^2 + 7*x^3 + 20*x^4 + 54*x^5 + 168*x^6 + 518*x^7 + 1702*x^8 + 5672*x^9 + 19413*x^10 + 67329*x^11 + ... + A322204(n)*x^n + ...

PROG

(PARI)

{L = sum(n=1, 61, -log(1 - (x^n + y^n) +O(x^61) +O(y^61)) ); }

{a(n) = polcoeff( n*polcoeff( L, n, x), n, y)}

for(n=1, 35, print1( a(n), ", ") )

CROSSREFS

Cf. A322204, A322202, A322200.

Sequence in context: A360798 A113835 A006349 * A052899 A147200 A147396

Adjacent sequences: A322200 A322201 A322202 * A322204 A322205 A322206

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 30 2018

STATUS

approved