This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A165937 G.f.: A(x) = exp( Sum_{n>=1} A002203(n^2)*x^n/n ). 4
 1, 2, 19, 964, 334965, 742714950, 10042408885191, 814556580116590856, 393147641272746246076745, 1123539400297807898234860367690, 18948227277012085227250633551784337179, 1881331163508674280605070386666674939623268684 (list; graph; refs; listen; history; text; internal format)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 10 23:18 EST 2019. Contains 329910 sequences. (Running on oeis4.)