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A119819
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a(n) is the coefficient of x^(n-1) in the (n-1)-th self-composition of g.f. A(x) for n>1, with a(1)=1.
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5
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1, 1, 2, 12, 138, 2370, 54190, 1553258, 53883088, 2211883428, 105760271082, 5819880201432, 364979361177134, 25865387272507770, 2056021496464455000, 182094050389241652004, 17861355920109599058260
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Here the zeroth self-composition of A(x) equals x, the first self-composition is itself, the 2nd self-composition of A(x) = A(A(x)), etc.
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EXAMPLE
| The successive self-compositions of g.f. A(x) begin:
A(x) = (1)x + x^2 + 2x^3 + 12x^4 + 138x^5 + 2370x^6 + 54190x^7 +...
A(A(x)) = x + (2)x^2 + 6x^3 + 35x^4 + 370x^5 + 6000x^6 + 132344x^7 +...
A(A(A(x))) = x + 3x^2 + (12)x^3 + 75x^4 + 758x^5 + 11612x^6 +...
A(A(A(A(x)))) = x + 4x^2 + 20x^3 + (138)x^4 + 1388x^5 + 20322x^6 +...
A(A(A(A(A(x))))) = x + 5x^2 + 30x^3 + 230x^4 + (2370)x^5 + 33760x^6+...
A(A(A(A(A(A(x)))))) = x + 6x^2 +42x^3 +357x^4 +3838x^5 + (54190)x^6+...
The diagonal of coefficients equals this sequence shift left 1 place.
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PROG
| (PARI) {a(n)=local(F=x+x^2+sum(m=3, n-1, a(m)*x^m), G=x+x*O(x^n)); if(n<1, 0, if(n<=2, 1, for(i=1, n-1, G=subst(F, x, G)); return(polcoeff(G, n-1, x))))}
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CROSSREFS
| Cf. A112317, A119820, A119821, A119815, A119817.
Sequence in context: A108996 A117513 A185522 * A093543 A091144 A087800
Adjacent sequences: A119816 A119817 A119818 * A119820 A119821 A119822
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 31 2006
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