A165937 G.f.: A(x) = exp( Sum_{n>=1} A002203(n^2)*x^n/n ).

1, 2, 19, 964, 334965, 742714950, 10042408885191, 814556580116590856, 393147641272746246076745, 1123539400297807898234860367690, 18948227277012085227250633551784337179, 1881331163508674280605070386666674939623268684

Offset

0,2

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).

Given g.f. A(x), (1-x)^(1/4) * A(x)^(1/8) is an integer series.

Links

Table of n, a(n) for n=0..11.

Formula

Logarithmic derivative equals A165938.

Self-convolution of A166879.

Example

G.f.: A(x) = 1 + 2*x + 19*x^2 + 964*x^3 + 334965*x^4 + 742714950*x^5 +...
log(A(x)) = 2*x + 34*x^2/2 + 2786*x^3/3 + 1331714*x^4/4 + 3710155682*x^5/5 + 60245508192802*x^6/6 + 5701755387019728962*x^7/7 +...+ A002203(n^2)*x^n/n +...

Prog

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

Crossrefs

Cf. A165938, A166879, A002203, A000129; variants: A158843, A166168, A155200.

Sequence in context: A013110 A024228 A015191 * A128345 A013052 A012956

Adjacent sequences: A165934 A165935 A165936 * A165938 A165939 A165940

Keyword

nonn

Author

Paul D. Hanna, Oct 18 2009

Status

approved