A307231 G.f.: A(x) = exp( Sum_{n>=1} x^n/n * (1 + x^n*A(x)^(2*n)) / (1 + x^n*A(x)^n) ).

1, 1, 1, 2, 3, 6, 14, 31, 74, 176, 425, 1055, 2637, 6671, 16995, 43507, 112102, 290347, 755836, 1976717, 5189664, 13673314, 36139543, 95795807, 254610593, 678385919, 1811625931, 4848177910, 12999914523, 34921821516, 93971264941, 253272232362, 683646029385, 1847935127768, 5001703392561, 13554768152442, 36777239050602, 99896764310264, 271633640605450, 739353335433377, 2014350935223715, 5493039157088226, 14992221809540249

Offset

0,4

Links

Paul D. Hanna, Table of n, a(n) for n = 0..300

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 6*x^5 + 14*x^6 + 31*x^7 + 74*x^8 + 176*x^9 + 425*x^10 + 1055*x^11 + 2637*x^12 + 6671*x^13 + 16995*x^14 + 43507*x^15 + ...
such that
log(A(x)) = x*(1 + x*A(x)^2)/(1 + x*A(x)) + x^2/2*(1 + x^2*A(x)^4)/(1 + x^2*A(x)^2) + x^3/3*(1 + x^3*A(x)^6)/(1 + x^3*A(x)^3) + x^4/4*(1 + x^4*A(x)^8)/(1 + x^4*A(x)^4) + x^5/5*(1 + x^5*A(x)^10)/(1 + x^5*A(x)^5) + ...
explicitly,
log(A(x)) = x + x^2/2 + 4*x^3/3 + 5*x^4/4 + 16*x^5/5 + 46*x^6/6 + 113*x^7/7 + 317*x^8/8 + 823*x^9/9 + 2206*x^10/10 + 6051*x^11/11 + 16418*x^12/12 + 45007*x^13/13 + 123033*x^14/14 + 336244*x^15/15 + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A=Vec( exp( sum(m=1, #A+1, x^m/m * (1 + x^m*Ser(A)^(2*m))/(1 + x^m*Ser(A)^m) ) )) ); A[n+1]}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Sequence in context: A335242 A032047 A032065 * A099968 A291401 A331875

Adjacent sequences: A307228 A307229 A307230 * A307232 A307233 A307234

Keyword

nonn

Author

Paul D. Hanna, Mar 29 2019

Status

approved