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

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]}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A306061, A316369.

Sequence in context: A356908 A032336 A032084 * A195967 A301602 A354898

Adjacent sequences: A306059 A306060 A306061 * A306063 A306064 A306065

Keyword

nonn

Author

Paul D. Hanna, Jun 19 2018

Status

approved