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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 (list; graph; refs; listen; history; text; internal format)
 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. LINKS Table of n, a(n) for n=0..16. 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 Cf. A108990, A108991, A108992, A108993, A108994, A108995. Sequence in context: A208873 A201561 A205886 * A117513 A343439 A297078 Adjacent sequences: A108993 A108994 A108995 * A108997 A108998 A108999 KEYWORD nonn AUTHOR Paul D. Hanna, Jun 15 2005 STATUS approved

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Last modified June 10 07:34 EDT 2023. Contains 363195 sequences. (Running on oeis4.)