A306061 L.g.f. A(x) satisfies: Sum_{n>=0} (log(1 + 2^n*x) - A(x))^n / n! = 1, where A(x) = Sum_{n>=1} a(n)*x^n/n.

2, 0, 68, 4200, 737432, 376015248, 596428719840, 3087194714985696, 54006009465104195072, 3279501822205862690687680, 705652071337358165341710594240, 546562572350657623752732853465340160, 1542500297504013104202649292306514734730496, 16012038105195898099786632602589693961733953444608, 615959454912822396904406370593148614749014922437494816768

Offset

1,1

Links

Table of n, a(n) for n=1..15.

Example

L.g.f. 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 + 54006009465104195072*x^9/9 + ...
such that Sum_{n>=0} (log(1 + 2^n*x) - A(x))^n / n!  =  1.
RELATED SERIES.
exp(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 + 327962184329946415530336*x^10 + ... + A306062(n)*x^n + ...

Prog

(PARI) {a(n) = my(A=[2]); for(i=1, n, A=concat(A, 0); A[#A] = Vec(sum(n=0, #A+1, (log(1 + 2^n*x +x*O(x^#A) ) - x*Ser(A))^n/n! ))[#A+1]); n*A[n]}
for(n=1, 20, print1(a(n), ", "))

Crossrefs

Cf. A306062.

Sequence in context: A140800 A012694 A264437 * A195209 A098276 A335692

Adjacent sequences: A306058 A306059 A306060 * A306062 A306063 A306064

Keyword

nonn

Author

Paul D. Hanna, Jun 18 2018

Status

approved