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A245932 G.f.: G'(x) / G(x) where G(x) = 1 / sqrt( AGM((1 - 3*x)^2, (1 + x)^2) ) is the g.f. of A245931. 3
1, 1, 1, 9, 41, 121, 281, 673, 2017, 6721, 21121, 61065, 171497, 495769, 1488761, 4509793, 13468897, 39688609, 116869153, 346788009, 1035199817, 3090560089, 9200749433, 27347417281, 81352371841, 242426988961, 723125351521, 2156829477609, 6430792717001, 19174372701241, 57194628447641 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Here AGM(x,y) = AGM((x+y)/2, sqrt(x*y)) denotes the arithmetic-geometric mean.

Limit a(n+1)/a(n) = 3.

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: A(x) = 1 + x + x^2 + 9*x^3 + 41*x^4 + 121*x^5 + 281*x^6 + 673*x^7 +...

As a logarithmic expansion,

L(x) = x + x^2/2 + x^3/3 + 9*x^4/4 + 41*x^5/5 + 121*x^6/6 + 281*x^7/7 + 673*x^8/8 + 2017*x^9/9 + 6721*x^10/10 +...

where

exp(L(x)) = 1 + x + x^2 + x^3 + 3*x^4 + 11*x^5 + 31*x^6 + 71*x^7 + 157*x^8 +...

equals 1 / sqrt( AGM((1 - 3*x)^2, (1 + x)^2) ).

PROG

(PARI) /* As the logarithmic derivative of A245931: */

{a(n)=local(G=1); G = 1 / sqrt( agm((1-3*x)^2, (1+x)^2 +x^2*O(x^n)) ); polcoeff(G'/G, n)}

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

(PARI) /* As the logarithm of g.f. of A245931 (offset = 1): */

{a(n)=local(A=1); A = -log( agm((1-3*x)^2, (1+x)^2 +x*O(x^n)) )/2; n*polcoeff(A, n)}

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

CROSSREFS

Cf. A245931.

Sequence in context: A273359 A251422 A018836 * A274323 A297740 A297741

Adjacent sequences:  A245929 A245930 A245931 * A245933 A245934 A245935

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Aug 14 2014

STATUS

approved

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Last modified March 26 23:07 EDT 2019. Contains 321566 sequences. (Running on oeis4.)