A323321 G.f. A(x) satisfies: 1 = Sum_{n>=0} ( (1+x)^n - 21*x*A(x) )^n * 10^n / 11^(n+1).

1, 230, 202720, 301356010, 609471837800, 1531246512757400, 4554410421462541300, 15575127764655971159900, 60061431635374301463364100, 257559473604548074955131621000, 1215330203862647096788767608162000, 6257647362127152791857282855542122000, 34917317338173226632480770480063290796000, 209923913089512941533199772776123546222790000, 1353013627656130991705167318085125179145490486000

Offset: 0

Author

Paul D. Hanna, Jan 10 2019

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 230*x + 202720*x^2 + 301356010*x^3 + 609471837800*x^4 + 1531246512757400*x^5 + 4554410421462541300*x^6 + 15575127764655971159900*x^7 + ...
such that
1 = 1/11 + ((1+x) - 21*x*A(x))*10/11^2 + ((1+x)^2 - 21*x*A(x))^2*10^2/11^3 + ((1+x)^3 - 21*x*A(x))^3*10^3/11^4 + ((1+x)^4 - 21*x*A(x))^4*10^4/11^5 + ...
Also,
1 = 1/(11 + 210*x*A(x)) + (1+x)*10/(11 + 210*x*A(x)*(1+x))^2 + (1+x)^4*10^2/(11 + 210*x*A(x)*(1+x)^2)^3 + (1+x)^9*10^3/(11 + 210*x*A(x)*(1+x)^3)^4 + ...
		

Crossrefs

Cf. A301435, A303288, A323314, A323315, A323316, A323317, A323318, A323319, A323320.

Programs

PARI

\p120
{A=vector(1); A[1]=1; for(i=1,20, A = concat(A,0);
A[#A] = round( Vec( sum(n=0, 3000, ( (1+x +x*O(x^#A))^n - 21*x*Ser(A) )^n * 10^n/11^(n+1)*1.)/210 ) )[#A+1]); A}

Formula

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

(1) 1 = Sum_{n>=0} ( (1+x)^n - 21*x*A(x) )^n * 10^n / 11^(n+1).

(2) 1 = Sum_{n>=0} (1+x)^(n^2) * 10^n / (11 + 210*x*A(x)*(1+x)^n)^(n+1).