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A323317 G.f. A(x) satisfies: 1 = Sum_{n>=0} ( (1+x)^n - 13*x*A(x) )^n * 6^n / 7^(n+1). 9
1, 90, 30360, 17260998, 13346871336, 12819352461768, 14575804541933076, 19054882926950474988, 28089490655708754330276, 46046879475849529578435672, 83060213421430745855381951856, 163488644041366509740041070551248, 348735916991281119541339971532867488, 801490465035993025759896936239032263600, 1974787497208210693752899355242321943894000, 5193543503462268857667579481311302800804588450 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..15.

FORMULA

G.f. A(x) satisfies the following identities.

(1) 1 = Sum_{n>=0} ( (1+x)^n - 13*x*A(x) )^n * 6^n / 7^(n+1).

(2) 1 = Sum_{n>=0} (1+x)^(n^2) * 6^n / (7 + 78*x*A(x)*(1+x)^n)^(n+1).

EXAMPLE

G.f.: A(x) = 1 + 90*x + 30360*x^2 + 17260998*x^3 + 13346871336*x^4 + 12819352461768*x^5 + 14575804541933076*x^6 + 19054882926950474988*x^7 + ...

such that

1 = 1/7 + ((1+x) - 13*x*A(x))*6/7^2 + ((1+x)^2 - 13*x*A(x))^2*6^2/7^3 + ((1+x)^3 - 13*x*A(x))^3*6^3/7^4 + ((1+x)^4 - 13*x*A(x))^4*6^4/7^5 + ...

Also,

1 = 1/(7 + 78*x*A(x)) + (1+x)*6/(7 + 78*x*A(x)*(1+x))^2 + (1+x)^4*6^2/(7 + 78*x*A(x)*(1+x)^2)^3 + (1+x)^9*6^3/(7 + 78*x*A(x)*(1+x)^3)^4 + ...

PROG

(PARI) \p120

{A=vector(1); A[1]=1; for(i=1, 20, A = concat(A, 0);

A[#A] = round( Vec( sum(n=0, 1200, ( (1+x +x*O(x^#A))^n - 13*x*Ser(A) )^n * 6^n/7^(n+1)*1.)/78 ) )[#A+1]); A}

CROSSREFS

Cf. A301435, A303288, A323314, A323315, A323316, A323318, A323319, A323320, A323321.

Sequence in context: A199229 A278411 A278631 * A246634 A270508 A134648

Adjacent sequences:  A323314 A323315 A323316 * A323318 A323319 A323320

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 10 2019

STATUS

approved

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Last modified October 6 04:09 EDT 2022. Contains 357261 sequences. (Running on oeis4.)