A366734 - OEIS

%I #5 Oct 29 2023 22:02:41

%S 1,4,24,236,2504,28332,335656,4108688,51558000,659737684,8575826448,

%T 112927383328,1503232394344,20195196226124,273467339844368,

%U 3728623506924660,51145851271818536,705322823588365592,9772995790887474920,135992755093954566300,1899633478390401668072

%N Expansion of g.f. A(x) satisfying 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (4 - x^(n-1))^(n+1).

%C a(n) = Sum_{k=0..n} A366730(n,k) * 4^k for n >= 0.

%F G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies the following formulas.

%F (1) 0 = Sum_{n=-oo..+oo} x^n * A(x)^n * (4 - x^(n-1))^(n+1).

%F (2) 0 = Sum_{n=-oo..+oo} (-1)^n * x^(n*(n-1)) / ( A(x)^n * (1 - 4*x^(n+1))^(n-1) ).

%e G.f.: A(x) = 1 + 4*x + 24*x^2 + 236*x^3 + 2504*x^4 + 28332*x^5 + 335656*x^6 + 4108688*x^7 + 51558000*x^8 + 659737684*x^9 + 8575826448*x^10 + ...

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

%o A[#A] = polcoeff( sum(n=-#A,#A, x^n * Ser(A)^n * (4 - x^(n-1))^(n+1) ), #A-2));A[n+1]}

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

%Y Cf. A366730, A366731, A366732, A366733, A366735.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 29 2023