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A322202 G.f.: exp( Sum_{n>=1} A322201(n)*x^n/n ), where A322201(n) is the coefficient of x^n*y^n/(2*n) in Sum_{n>=1} -log(1 - (x^n + y^n)). 4
1, 2, 7, 20, 63, 190, 613, 1976, 6604, 22368, 77270, 270208, 956780, 3419212, 12323226, 44723840, 163320766, 599601984, 2211844684, 8193734760, 30469278673, 113692852342, 425558528235, 1597428832560, 6011972255226, 22680620270712, 85754229105470, 324898592591960, 1233299357981416, 4689870496585016, 17863799895741982, 68149300647823612, 260364494604701847, 996086232267182566, 3815683108118138847, 14634441964549504036 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

EXAMPLE

G.f.: A(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 + ...

such that

log( A(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 + ... + A322201(n)*x^n/n + ...

sqrt(A(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 + 236994*x^12 + ... + A322204(n)*x^n + ...

PROG

(PARI)

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

{A322201(n) = polcoeff( 2*n*polcoeff( L, n, x), n, y)}

{a(n) = polcoeff( exp( sum(m=1, n, A322201(m)*x^m/m ) +x*O(x^n) ), n) }

for(n=0, 35, print1( a(n), ", ") )

CROSSREFS

Cf. A322200, A322201, A322204.

Sequence in context: A014983 A083379 A216246 * A000935 A035071 A055891

Adjacent sequences:  A322199 A322200 A322201 * A322203 A322204 A322205

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 30 2018

STATUS

approved

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Last modified March 25 07:12 EDT 2019. Contains 321468 sequences. (Running on oeis4.)