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%I #12 Apr 28 2017 18:26:23
%S 1,1,16,25,36,100,225,441,961,2116,4489,9604,20736,44521,95481,205209,
%T 440896,946729,2033476,4368100,9381969,20151121,43283241,92968164,
%U 199685161,428904100,921243904,1978737289,4250127249,9128847025,19607840784,42115658841
%N a(n) = A001609(n)^2, where g.f. of A001609 is x*(1+3*x^2)/(1-x-x^3).
%C A001609 equals the logarithmic derivative of Narayana's cows sequence A000930.
%H G. C. Greubel, <a href="/A218439/b218439.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,3,1,-1,-1).
%F O.g.f.: x*(1 + 14*x^2 + 5*x^3 - 9*x^4 - 9*x^5)/((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)).
%F Logarithmic derivative of A218438.
%F a(n) = -2*(-1)^n*A112455(n) +3*A002478(n) -2*A002478(n-1)-2*A002478(n-2), n>1. - _R. J. Mathar_, Oct 28 2012
%e O.g.f.: A(x) = x + x^2 + 16*x^3 + 25*x^4 + 36*x^5 + 100*x^6 + 225*x^7 +...
%e L.g.f.: L(x) = x + x^2/2 + 16*x^3/3 + 25*x^4/4 + 36*x^5/5 + 100*x^6/6 + 225*x^7/7 +...
%e where exponentiation yields the g.f. of A218438:
%e exp(L(x)) = 1 + x + x^2 + 6*x^3 + 12*x^4 + 19*x^5 + 48*x^6 + 110*x^7 +...
%t Rest[CoefficientList[Series[x*(1 + 14*x^2 + 5*x^3 - 9*x^4 - 9*x^5)/((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)), {x, 0, 50}], x]] (* _G. C. Greubel_, Apr 28 2017 *)
%o (PARI) {a(n)=polcoeff(x*(1+14*x^2+5*x^3-9*x^4-9*x^5)/((1+x^2-x^3)*(1-x-2*x^2-x^3+x*O(x^n))),n)}
%o for(n=1,40,print1(a(n),", "))
%Y Cf. A000930, A001609, A002478, A112455, A218438.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Oct 28 2012
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