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 A193111 G.f. satisfies: 1 = Sum_{n>=0} (-x)^(n*(n+1)/2) * A(x)^(n+1). 6
 1, 1, 2, 6, 19, 63, 218, 781, 2869, 10742, 40846, 157318, 612446, 2406100, 9527159, 37981611, 152328497, 614167702, 2487941464, 10121128882, 41330709103, 169362297620, 696187639438, 2870017515884, 11862845007114, 49152859179055 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Paul D. Hanna, Table of n, a(n) for n = 0..300 FORMULA G.f. A(x) satisfies the continued fraction: 1 = A(x)/(1+ x*A(x)/(1- x*(1+x)*A(x)/(1+ x^3*A(x)/(1+ x^2*(1-x^2)*A(x)/(1+ x^5*A(x)/(1- x^3*(1+x^3)*A(x)/(1+ x^7*A(x)/(1+ x^4*(1-x^4)*A(x)/(1- ...))))))))) due to an identity of a partial elliptic theta function. EXAMPLE G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 19*x^4 + 63*x^5 + 218*x^6 +... which satisfies: 1 = A(x) - x*A(x)^2 - x^3*A(x)^3 + x^6*A(x)^4 + x^10*A(x)^5 - x^15*A(x)^6 - x^21*A(x)^7 ++--... Related expansions. A(x)^2 = 1 + 2*x + 5*x^2 + 16*x^3 + 54*x^4 + 188*x^5 + 674*x^6 +... A(x)^3 = 1 + 3*x + 9*x^2 + 31*x^3 + 111*x^4 + 405*x^5 + 1505*x^6 +... PROG (PARI) {a(n)=local(A=[1]); for(i=1, n, A=concat(A, 0); A[#A]=polcoeff(1-sum(m=0, sqrtint(2*(#A))+1, (-x)^(m*(m+1)/2)*Ser(A)^(m+1)), #A-1)); if(n<0, 0, A[n+1])} CROSSREFS Cf. A193112, A193113, A193114, A193115, A193116. Sequence in context: A141771 A001170 A001168 * A119255 A071969 A063030 Adjacent sequences:  A193108 A193109 A193110 * A193112 A193113 A193114 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 16 2011 STATUS approved

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Last modified October 17 11:58 EDT 2019. Contains 328110 sequences. (Running on oeis4.)