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Search: id:A088714
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| A088714 |
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G.f. satisfies: A(x) = 1 + x*A(x)^2*A(x*A(x)). |
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+0
11
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| 1, 1, 3, 13, 69, 419, 2809, 20353, 157199, 1281993, 10963825, 97828031, 907177801, 8716049417, 86553001779, 886573220093, 9351927111901, 101447092428243, 1130357986741545, 12923637003161409, 151479552582252239
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f.: A(x) = f(x*A(x)) = (1-1/f(x))/x where f(x) is the g.f. of A088713.
Given g.f. A(x), then B(x)=x*A(x) satisfies 0=f(x, B(x), B(B(x))) where f(a0, a1, a2)=a0-a1+a1*a2 . - Michael Somos May 21 2005
G.f. satisfies: A(x) = 1/(1 - x*A(x)*A(x*A(x))).
G.f. satisfies: A(x) = (1/x)*Series_Reversion(x - x^2*A(x)).
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EXAMPLE
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Comment from Paul D. Hanna (pauldhanna(AT)juno.com), Apr 16 2007: G.f. A(x) is the unique solution to variable A in the infinite system of simultaneous equations:
A = 1 + xAB;
B = A + xBC;
C = B + xCD;
D = C + xDE;
E = D + xEF ; ...
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, n++; A=x+O(x^2); for(i=2, n, A=x/(1-subst(A, x, A))); polcoeff(A, n))} /* Michael Somos May 21 2005 */
(PARI) {a(n)=local(A); if(n<0, 0, A=1+x+O(x^2); for(i=1, n, A=1/(1-x*A*subst(A, x, x*A))); polcoeff(A, n))}
(PARI) {a(n)=local(A); if(n<0, 0, A=1+x+O(x^2); for(i=0, n, A=(1/x)*serreverse(x-x^2*A)); polcoeff(A, n))}
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CROSSREFS
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Cf. A088713.
Apart from signs, same as A067145. - Philippe DELEHAM, Jun 18 2006
Cf. A002449, A030266, A087949, A088717, A091713, A120971.
Adjacent sequences: A088711 A088712 A088713 this_sequence A088715 A088716 A088717
Sequence in context: A128079 A074534 A067145 this_sequence A088368 A007808 A104989
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Oct 12 2003, May 22 2008
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