A397243 - OEIS

%I #9 Jun 22 2026 11:11:01

%S 1,3,40,915,30816,1413930,84513360,6384139587,595609853440,

%T 67353819584238,9087133029153840,1442929646432008878,

%U 266495181531171493824,56660732059178616326100,13743303287006807329982880,3772610857852397449962995235,1163717696949502364569525508352,400819880895705955239599615666790

%N L.g.f. Sum_{n>=1} a(n)*x^n/n = log(1+x + Sum_{n>=2} n/(n^2-1) * a(n)*x^n ).

%H Paul D. Hanna, <a href="/A397243/b397243.txt">Table of n, a(n) for n = 1..500</a>

%F Forms the logarithmic derivative of the g.f. of A397242.

%F a(n) = (n^2-1)/n * A397242(n) for n > 1 with a(1) = 1.

%e L.g.f.: L(x) = x + 3*x^2/2 + 40*x^3/3 + 915*x^4/4 + 30816*x^5/5 + 1413930*x^6/6 + 84513360*x^7/7 + 6384139587*x^8/8 + ...

%e where

%e exp(L(x)) = 1 + x + 2*x^2 + 15*x^3 + 244*x^4 + 6420*x^5 + 242388*x^6 + 12324865*x^7 + ... + n/(n^2-1) * a(n)*x^n + ...

%o (PARI) {a(n) = my(L=[0,1],A,m); for(i=2,n, L=concat(L,0); A = exp(Ser(L)); m = #L-1;

%o L[#L] = (m^2-1)*polcoef(A,m) - m^2*polcoef(log(A),m) ); GF=Ser(L); L[n+1]}

%o \\ returns a vector of terms a(k) for k = 1..n

%o {upto(n) = a(n); Vec(GF')}

%o upto(25)

%Y Cf. A397241, A397242.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Jun 19 2026