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A153849 a(n) is the coefficient of x^n in the (n+2)-th self-composition of g.f. A(x) for n>=1, with a(1)=1. 0
1, 1, 4, 40, 675, 16023, 488264, 18150408, 798091737, 40691618165, 2372928554920, 156676126511294, 11619829396974162, 961567152709817189, 88268869225674860344, 8941327301073770038304, 994670849523023025795108 (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 + 4*x^3 + 40*x^4 + 675*x^5 + 16023*x^6 +...

Coefficients of successive iterations of A(x) are as follows:

[1,1,4,40,675,16023,488264,18150408,798091737,40691618165,...];

[1,2,10,101,1658,38327,1144412,41900873,1821202358,...];

[(1),3,18,189,3063,69204,2024472,72937181,3130859853,...];

[1,(4),28,310,5028,111648,3202916,113479712,4806652072,...];

[1,5,(40),470,7715,169475,4777592,166446886,6951781033,...];

[1,6,54,(675),11310,247443,6875376,235657813,9700212066,...];

[1,7,70,931,(16023),351372,9658544,326079187,13225766705,...];

[1,8,88,1244,22088,(488264),13331864,444121464,17753548560,...];

[1,9,108,1620,29763,666423,(18150408),597989364,23574131721,...];

[1,10,130,2065,39330,895575,24428084,(798091737),31060981566,...];

[1,11,154,2585,51095,1186988,32546888,1057515833,(40691618165),...];

where the diagonal of terms in parenthesis form this sequence.

Some explicit expansions:

A(A(x)) = x + 2*x^2 + 10*x^3 + 101*x^4 + 1658*x^5 + 38327*x^6 +...;

A(A(A(x))) = x + 3*x^2 + 18*x^3 + 189*x^4 + 3063*x^5 + 69204*x^6 +...;

A(A(A(A(x)))) = x + 4*x^2 + 28*x^3 + 310*x^4 + 5028*x^5 + 111648*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+1, G=subst(F, x, G)); return(polcoeff(G, n-1, x))))}

CROSSREFS

Cf. A119819, A153389.

Sequence in context: A234294 A181088 A005431 * A251574 A010792 A064422

Adjacent sequences:  A153846 A153847 A153848 * A153850 A153851 A153852

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 04 2009

STATUS

approved

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Last modified April 22 11:46 EDT 2019. Contains 322330 sequences. (Running on oeis4.)