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 A245389 G.f. satisfies: A(x) = Sum_{n>=0} x^n / (1 - (n+1)*x*A(x)). 2
 1, 2, 6, 23, 102, 496, 2570, 13959, 78682, 457243, 2727360, 16647048, 103759186, 659500772, 4271197824, 28175622291, 189321228022, 1296246842443, 9049626101836, 64481397834665, 469461395956168, 3497006117588399, 26688813841105524, 208977790442594368, 1680981707733908594 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Paul D. Hanna, Table of n, a(n) for n = 0..300 FORMULA G.f. A(x) satisfies: (1) A(x) = Sum_{n>=0} x^n / (1 - (n+1)*x*A(x)). (2) A(x) = Sum_{n>=0} n! * x^n/(1-x)^(n+1) * A(x)^n / Product_{k=1..n} (1 + k*x*A(x)). EXAMPLE G.f.: A(x) = 1 + 2*x + 6*x^2 + 23*x^3 + 102*x^4 + 496*x^5 + 2570*x^6 +... where we have the following series identity: A(x) = 1/(1-x*A(x)) + x/(1-2*x*A(x)) + x^2/(1-3*x*A(x)) + x^3/(1-4*x*A(x)) + x^4/(1-5*x*A(x)) + x^5/(1-6*x*A(x)) + x^6/(1-7*x*A(x)) +... is equal to A(x) = 1/(1-x) + x/(1-x)^2*A(x)/(1+x*A(x)) + 2!*x^2/(1-x)^3*A(x)^2/((1+x*A(x))*(1+2*x*A(x))) + 3!*x^3/(1-x)^4*A(x)^3/((1+x*A(x))*(1+2*x*A(x))*(1+3*x*A(x))) + 4!*x^4/(1-x)^5*A(x)^4/((1+x*A(x))*(1+2*x*A(x))*(1+3*x*A(x))*(1+4*x*A(x))) + 5!*x^5/(1-x)^6*A(x)^5/((1+x*A(x))*(1+2*x*A(x))*(1+3*x*A(x))*(1+4*x*A(x))*(1+5*x*A(x))) +... PROG (PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, x^m/(1-(m+1)*x*A+x*O(x^n)))); polcoeff(A, n)} for(n=0, 30, print1(a(n), ", ")) (PARI) {a(n)=local(A=1+x); for(i=1, n, A=sum(m=0, n, m!*x^m*A^m/(1-x +x*O(x^n))^(m+1)/prod(k=1, m, 1+k*x*A +x*O(x^n)))); polcoeff(, n)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A026898, A316367. Sequence in context: A120346 A050389 A098746 * A088929 A279573 A174193 Adjacent sequences:  A245386 A245387 A245388 * A245390 A245391 A245392 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 20 2014 STATUS approved

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Last modified April 4 04:47 EDT 2020. Contains 333212 sequences. (Running on oeis4.)