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A153389 a(n) is the coefficient of x^n in the (n+1)-th self-composition of g.f. A(x) for n>=1, with a(1)=1. 1
1, 1, 3, 24, 340, 6950, 185332, 6102096, 240066324, 11049803253, 586427736400, 35496295553400, 2429241782433336, 186578739919860938, 15978032482994396274, 1516714259732732880752, 158739955140174552148004 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..17.

EXAMPLE

G.f.: A(x) = x + x^2 + 3*x^3 + 24*x^4 + 340*x^5 + 6950*x^6 +...

The initial coefficients of successive iterations of A(x) are as follows:

[1,1,3,24,340,6950,185332,6102096,240066324,11049803253,...];

[(1),2,8,64,866,17042,442452,14294645,554552353,25248014932,...];

[1,(3),15,126,1666,31676,799438,25293855,966179243,...];

[1,4,(24),216,2852,52800,1295784,40085834,1505339722,...];

[1,5,35,(340),4560,83030,1986288,60029146,2212932714,...];

[1,6,48,504,(6950),125770,2945660,86988543,3144212187,...];

[1,7,63,714,10206,(185332),4273850,123504913,4373929873,...];

[1,8,80,976,14536,267056,(6102096),173006484,6003091828,...];

[1,9,99,1296,20172,377430,8599692,(240066324),8167689120,...];

[1,10,120,1680,27370,524210,11981476,330711177,(11049803253),...];...

where the diagonal of terms in parenthesis form this sequence.

Some explicit expansions:

A(A(x)) = x + 2*x^2 + 8*x^3 + 64*x^4 + 866*x^5 + 17042*x^6 +...;

A(A(A(x))) = x + 3*x^2 + 15*x^3 + 126*x^4 + 1666*x^5 + 31676*x^6 +...;

A(A(A(A(x)))) = x + 4*x^2 + 24*x^3 + 216*x^4 + 2852*x^5 + 52800*x^6 +...;

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, G=subst(F, x, G)); return(polcoeff(G, n-1, x))))}

CROSSREFS

Cf. A119819.

Sequence in context: A082166 A144003 A334775 * A332975 A010791 A145169

Adjacent sequences:  A153386 A153387 A153388 * A153390 A153391 A153392

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 04 2009

STATUS

approved

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Last modified September 26 16:43 EDT 2020. Contains 337374 sequences. (Running on oeis4.)