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a(n) = A359720(n+3,2), for n >= 0.
2

%I #5 Jan 14 2023 10:51:54

%S 1,9,49,179,711,2390,8361,27082,89389,283170,905307,2825245,8854116,

%T 27341969,84550769,259046260,793589833,2416512240,7352490113,

%U 22279068811,67435591018,203525629398,613550161717,1845654390776,5545861291941,16637001197044,49858191850323

%N a(n) = A359720(n+3,2), for n >= 0.

%C The g.f. of A359720, G(x,y) = Sum_{n>=0} Sum_{k=0..floor(2*n/3)} A359720(n,k)*x^n*y^k, satisfies: x = Sum_{n=-oo..+oo} (-1)^n * x^n * (y + x^n)^n * G(x,y)^n.

%o (PARI) /* a(n) = A359720(n+3,2) */

%o {a(n) = my(A=[1]); for(i=1, n+3, A=concat(A, 0);

%o A[#A] = polcoeff(x - sum(m=-#A, #A, (-1)^m * x^m * (y + x^m +x*O(x^#A) )^m * Ser(A)^m ), #A-1) );

%o polcoeff( polcoeff(Ser(A), n+3,x), 2,y)}

%o for(n=0, 30, print1(a(n), ", "))

%Y Cf. A359720, A355357, A359725.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 14 2023