Original entry on oeis.org
2, 34, 2786, 1331714, 3710155682, 60245508192802, 5701755387019728962, 3145168096065837266706434, 10111847525912679844192131854786, 189482250299273866835746159841800035874, 20694642381734231604510939638726181796865594402
Offset: 1
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Simplify[Table[(1 + Sqrt[2])^(n^2) + (1 - Sqrt[2])^(n^2), {n, 1, 7}]] (* G. C. Greubel, Apr 18 2016 *)
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{a(n)=polcoeff(2*(1-x)/(1-2*x-x^2 +x*O(x^(n^2))),n^2)}
A204327
a(n) = Pell(n^2).
Original entry on oeis.org
1, 12, 985, 470832, 1311738121, 21300003689580, 2015874949414289041, 1111984844349868137938112, 3575077977948634627394046618865, 66992092050551637663438906713182313772, 7316660981177400006023755031791634132229378601
Offset: 1
G.f.: A(x) = x + 12*x^2 + 985*x^3 + 470832*x^4 + 1311738121*x^5 +...
A166879
G.f.: A(x) = exp( Sum_{n>=1} A002203(n^2)/2*x^n/n ).
Original entry on oeis.org
1, 1, 9, 473, 166969, 371186249, 5020831641761, 407273265807001089, 196573413317730320842177, 561769503571822735164882969633, 9474113076734769687535254457293566857, 940665572280219007549184269220597591870817337
Offset: 0
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 +...
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{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))}
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{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)))}
A158843
G.f.: A(x) = exp( Sum_{n>=1} A001333(n)^n * 2^n*x^n/n ).
Original entry on oeis.org
1, 2, 20, 952, 336112, 742166496, 10043945021760, 814531629739559808, 393150002983518264270592, 1123538097532735360702239462912, 18948231465474675384343860006353603584, 1881331085022567366434813565917484763975526400
Offset: 0
G.f.: A(x) = 1 + 2*x + 20*x^2 + 952*x^3 + 336112*x^4 + 742166496*x^5 +...
log(A(x)) = 2*x + 6^2*x^2/2 + 14^3*x^3/3 + 34^4*x^4/4 + 82^5*x^5/5 +...
log(G(x)) = 2*x + 6*x^2/2 + 14*x^3/3 + 34*x^4/4 + 82*x^5/5 +...
G(x) = 1 + 2*x + 5*x^2 + 12*x^3 + 29*x^4 + 70*x^5 + 169*x^6 +... (A000129).
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{a(n)=local(LD=Vec(2*(1+x)/(1-2*x-x^2 +x*O(x^n)))); polcoeff(exp(sum(m=1,n,LD[m]^m*x^m/m)+x*O(x^n)),n)}
Showing 1-4 of 4 results.
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