0,3

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.

In the table of successive self-convolutions:

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

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

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

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

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

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

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

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

(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)}

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

Sequence in context: A080487 A077696 A117271 this_sequence A117513 A119819 A093543

Adjacent sequences: A108993 A108994 A108995 this_sequence A108997 A108998 A108999

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Jun 15 2005