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A108996
G.f.: A(x) = x/series_reversion(x*G108993(x)) where G108993(x) is g.f. of A108993.
6
1, 1, 2, 12, 136, 2295, 51827, 1475418, 50941044, 2075342121, 97720284626, 5232249371767, 314410678948598, 20975495941289630, 1539572666035763341, 123374691634976163059, 10723345155948465053752
OFFSET
0,3
COMMENTS
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.
EXAMPLE
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,...
PROG
(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)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 15 2005
STATUS
approved