A306062 - OEIS

A306062

O.g.f. A(x) satisfies: Sum_{n>=0} log( (1 + 2^n*x) / A(x) )^n / n! = 1.

1, 2, 2, 24, 1096, 149632, 62966568, 85329761952, 386069877057040, 6001439689098721408, 327962184329946415530336, 64150844215771337825753078272, 45547009330254120256598494596400320, 118653960132660605481807477808249363616768, 1143717244821821894255831791273094878164139953920, 41063965948289078797110473909472925848872401288025550336

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..15.

EXAMPLE

O.g.f. A(x) = 1 + 2*x + 2*x^2 + 24*x^3 + 1096*x^4 + 149632*x^5 + 62966568*x^6 + 85329761952*x^7 + 386069877057040*x^8 + 6001439689098721408*x^9 + ...

such that Sum_{n>=0} log( (1 + 2^n*x) / A(x) )^n / n! = 1.

RELATED SERIES.

log(A(x)) = 2*x + 68*x^3/3 + 4200*x^4/4 + 737432*x^5/5 + 376015248*x^6/6 + 596428719840*x^7/7 + 3087194714985696*x^8/8 + ... + A306061(n)*x^n/n + ...

PROG

(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A] = Vec( sum(m=0, #A, log( (1+2^m*x +x*O(x^#A)) / Ser(A) )^m/m! ) )[#A] ); A[n+1]}