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 A190790 G.f. satisfies: A(x) = 1 + Sum_{n>=1} q^(2n-1)/(1 - q^(2n-1)) where q = x*A(x). 2
 1, 1, 2, 6, 18, 58, 198, 696, 2506, 9205, 34344, 129792, 495834, 1911640, 7428444, 29064650, 114404410, 452719183, 1799994588, 7187148262, 28807364008, 115865980972, 467497031164, 1891710323324, 7675031497682, 31215088847239 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS FORMULA G.f. A(x) satisfies: * A(x) = 1 + Sum_{n>=1} q^(n*(n+1)/2)/(1 - q^n), where q = x*A(x); * A(x) = 1 + Sum_{n>=1} q^n/(1 - q^(2n)), where q = x*A(x); * A(x) = 1 + Sum_{n>=1} A001227(n)*x^n*A(x)^n, where A001227(n) = number of odd divisors of n. Let D(x) = 1 + Sum_{n>=1} A001227(n)*x^n, then * A(x) = D(x*A(x)) and D(x) = A(x/D(x)); * A(x) = (1/x)*Series_Reversion(x/D(x)); * a(n) = [x^n] D(x)^(n+1)/(n+1), the coefficient of x^n in D(x)^(n+1)/(n+1) for n>=0. EXAMPLE G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 18*x^4 + 58*x^5 + 198*x^6 +... Let q = x*A(x), then the g.f. A(x) satisfies the following series: * A(x) = 1 + q/(1 - q) + q^3/(1 - q^3) + q^5/(1 - q^5) + q^7/(1 - q^7) +... * A(x) = 1 + q/(1 - q) + q^3/(1 - q^2) + q^6/(1 - q^3) + q^10/(1 - q^4) +... * A(x) = 1 + q/(1 - q^2) + q^2/(1 - q^4) + q^3/(1 - q^6) + q^4/(1 - q^8) +... * A(x) = 1 + q + q^2 + 2*q^3 + q^4 + 2*q^5 + 2*q^6 +...+ A001227(n)*q^n +... PROG (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, (x*A)^(2*m-1)/(1-(x*A)^(2*m-1)+x*O(x^n)))); polcoeff(A, n)} (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, (x*A)^(m*(m+1)/2)/(1-(x*A)^m+x*O(x^n)))); polcoeff(A, n)} (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, (x*A)^m/(1-(x*A)^(2*m)+x*O(x^n)))); polcoeff(A, n)} (PARI) {a(n)=local(D=1+sum(m=1, n, sumdiv(m, d, d%2)*x^m)+x*O(x^n)); polcoeff(1/x*serreverse(x/D), n)} (PARI) {a(n)=local(D=1+sum(m=1, n, sumdiv(m, d, d%2)*x^m)+x*O(x^n)); polcoeff(D^(n+1)/(n+1), n)} CROSSREFS Sequence in context: A293067 A085139 A150041 * A150042 A036675 A227373 Adjacent sequences:  A190787 A190788 A190789 * A190791 A190792 A190793 KEYWORD nonn AUTHOR Paul D. Hanna, May 20 2011 STATUS approved

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Last modified November 27 03:56 EST 2021. Contains 349345 sequences. (Running on oeis4.)