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 A190861 G.f. satisfies: A(x) = Product_{n>=1} (1 + x^n*A(x))/(1-x^n). 2
 1, 2, 6, 18, 56, 178, 580, 1922, 6466, 22022, 75788, 263152, 920768, 3243414, 11492460, 40934616, 146484296, 526389182, 1898722242, 6872300848, 24951521464, 90851221740, 331666951116, 1213729811070, 4451547793956 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n*Product_{k=1..n} (1 + x^(k-1)*A(x))/(1-x^k) due to the q-binomial theorem. EXAMPLE G.f.: A(x) = 1 + 2*x + 6*x^2 + 18*x^3 + 56*x^4 + 178*x^5 + 580*x^6 +... such that the g.f. satisfies the identity: A(x) = (1+x*A(x))/(1-x) * (1+x^2*A(x))/(1-x^2) * (1+x^3*A(x))/(1-x^3) *... A(x) = 1 + x*(1+A(x))/(1-x) + x^2*(1+A(x))*(1+x*A(x))/((1-x)*(1-x^2)) + x^3*(1+A(x))*(1+x*A(x))*(1+x^2*A(x))/((1-x)*(1-x^2)*(1-x^3)) +... PROG (PARI) {a(n)=local(A=1+x); for(i=1, n, A=prod(m=1, n, (1+x^m*A)/(1-x^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^m*prod(k=1, m, (1+x^(k-1)*A)/(1-x^k+x*O(x^n))))); polcoeff(A, n)} CROSSREFS Cf. A209357, A190862. Sequence in context: A091142 A275857 A111961 * A071721 A125306 A209797 Adjacent sequences:  A190858 A190859 A190860 * A190862 A190863 A190864 KEYWORD nonn AUTHOR Paul D. Hanna, May 21 2011 STATUS approved

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Last modified August 1 06:45 EDT 2021. Contains 346384 sequences. (Running on oeis4.)