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A166879 G.f.: A(x) = exp( Sum_{n>=1} A002203(n^2)/2*x^n/n ). 3
1, 1, 9, 473, 166969, 371186249, 5020831641761, 407273265807001089, 196573413317730320842177, 561769503571822735164882969633, 9474113076734769687535254457293566857, 940665572280219007549184269220597591870817337 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A002203 equals the logarithmic derivative of the Pell numbers (A000129).

Note that A002203(n^2) = (1+sqrt(2))^(n^2) + (1-sqrt(2))^(n^2).

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..40

FORMULA

a(n) == 1 (mod 8).

a(n) = (1/n)*Sum_{k=1..n} A002203(k^2)/2*a(n-k) for n>0 with a(0)=1.

Self-convolution yields A165937.

EXAMPLE

G.f.: A(x) = 1 + x + 9*x^2 + 473*x^3 + 166969*x^4 + 371186249*x^5 +...

log(A(x)) = x + 17*x^2/2 + 1393*x^3/3 + 665857*x^4/4 + 1855077841*x^5/5 + 30122754096401*x^6/6 + 2850877693509864481*x^7/7 +...+ A002203(n^2)/2*x^n/n +...

PROG

(PARI) {a(n)=if(n==0, 1, polcoeff(exp(sum(m=1, n, polcoeff((1-x)/(1-2*x-x^2+x*O(x^(m^2))), m^2)*x^m/m)+x*O(x^n)), n))}

(PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, polcoeff((1-x)/(1-2*x-x^2+x*O(x^(k^2))), k^2)*a(n-k)))}

CROSSREFS

Cf. A165937, A165938, A002203, A000129.

Sequence in context: A285371 A061175 A289054 * A213447 A128947 A293951

Adjacent sequences:  A166876 A166877 A166878 * A166880 A166881 A166882

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 22 2009

STATUS

approved

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Last modified March 28 13:15 EDT 2020. Contains 333089 sequences. (Running on oeis4.)