A108996 - OEIS

%I #4 Mar 30 2012 18:36:49

%S 1,1,2,12,136,2295,51827,1475418,50941044,2075342121,97720284626,

%T 5232249371767,314410678948598,20975495941289630,1539572666035763341,

%U 123374691634976163059,10723345155948465053752

%N G.f.: A(x) = x/series_reversion(x*G108993(x)) where G108993(x) is g.f. of A108993.

%C A108993 is derived from the second diagonal (A108992) of triangle A108990, in which the g.f. of row n, R_n(x), satisfies: [x^k] R_{n+1}(x) = [x^k] (1 + x*R_n(x))^(n+1) for k=0..n+1.

%e In the table of successive self-convolutions:

%e 1,1,2,12,136,2295,51827,1475418,...

%e 1,2,5,28,300,4910,108932,3066934,...

%e 1,3,9,49,498,7893,171875,4783641,...

%e 1,4,14,76,737,11300,241288,6635496,...

%e 1,5,20,110,1025,15196,317885,8633420,...

%e 1,6,27,152,1371,19656,402473,10789410,...

%e 1,7,35,203,1785,24766,495964,13116664,...

%e the main diagonal is equal to A108992: 1,2,9,76,1025,19656,495964,15629720,...

%o (PARI) {a(n)=local(F=1+x*O(x^n),G=0);for(m=0,n, for(k=1,m+1,F=(1+x*F)^k); G=G+polcoeff(F,m)/(m+1)*x^m);F=x/serreverse(x*Ser(G));polcoeff(F,n)}

%Y Cf. A108990, A108991, A108992, A108993, A108994, A108995.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 15 2005