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 A193038 G.f. A(x) satisfies: x = Sum_{n>=1} x^n*A(-x)^sigma(n), where sigma(n) = sum of divisors of n (A000203). 2
 1, 1, 2, 6, 23, 101, 475, 2321, 11629, 59364, 307648, 1614724, 8567810, 45890927, 247817187, 1347819147, 7376472346, 40594360200, 224500075274, 1247028876157, 6954322550810, 38921347036195, 218541728743211, 1230754878156173, 6950114772716368 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Compare the g.f. to a g.f. C(x) of the Catalan numbers: x = Sum_{n>=1} x^n*C(-x)^(2*n-1). LINKS EXAMPLE G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 23*x^4 + 101*x^5 + 475*x^6 +... The g.f. satisfies: x = x*A(-x) + x^2*A(-x)^3 + x^3*A(-x)^4 + x^4*A(-x)^7 + x^5*A(-x)^6 + x^6*A(-x)^12 +...+ x^n*A(-x)^A000203(n) +... where A000203 begins: [1,3,4,7,6,12,8,15,13,18,12,28,14,24,24,31,...]. PROG (PARI) {a(n)=local(A=[1]); for(i=1, n, A=concat(A, 0); A[#A]=polcoeff(sum(m=1, #A, (-x)^m*Ser(A)^sigma(m)), #A)); if(n<0, 0, A[n+1])} CROSSREFS Cf. A193036, A193037, A193039, A193040, A000203. Sequence in context: A233106 A133656 A078487 * A213090 A218225 A279572 Adjacent sequences:  A193035 A193036 A193037 * A193039 A193040 A193041 KEYWORD nonn AUTHOR Paul D. Hanna, Jul 14 2011 STATUS approved

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Last modified September 17 01:53 EDT 2021. Contains 347478 sequences. (Running on oeis4.)