A273957 - OEIS

%I #9 Mar 19 2025 15:03:18

%S 1,1,2,7,31,159,909,5657,37750,267367,1995167,15601743,127317160,

%T 1080705251,9517003663,86763537749,817415449402,7946161682759,

%U 79599437483758,820726329776013,8701095694308761,94761241694697957,1059246307095497960,12143075480602664161,142660989450995958519,1716427548002953822635,21135147232385131769271

%N G.f. A(x) satisfies: A(x - x/(1+x)*A(x)) = x.

%F G.f. A(x) satisfies:

%F (1) A(x) = x + Sum_{n>=1} (d/dx)^(n-1) ( x/(1+x)*A(x) )^n / n!.

%F (2) A(x) = x * exp( Sum_{n>=1} (d/dx)^(n-1) (1/x) * ( x/(1+x)*A(x) )^n / n! ).

%e G.f.: A(x) = x + x^2 + 2*x^3 + 7*x^4 + 31*x^5 + 159*x^6 + 909*x^7 + 5657*x^8 + 37750*x^9 + 267367*x^10 + 1995167*x^11 + 15601743*x^12 +...

%o (PARI) {a(n) = my(A=x); for(i=1,n, A = serreverse(x - x/(1+x)*A +x*O(x^n)) ); polcoeff(A,n)}

%o for(n=1,30,print1(a(n),", "))

%K nonn,changed

%O 1,3

%A _Paul D. Hanna_, Jun 10 2016