A108996 G.f.: A(x) = x/series_reversion(x*G108993(x)) where G108993(x) is g.f. of A108993.

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.

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