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 A246432 Convolution inverse of A001700. 4
 1, -3, -1, -2, -5, -14, -42, -132, -429, -1430, -4862, -16796, -58786, -208012, -742900, -2674440, -9694845, -35357670, -129644790, -477638700, -1767263190, -6564120420, -24466267020, -91482563640, -343059613650, -1289904147324, -4861946401452 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1660 FORMULA G.f.: (1 + sqrt(1 - 4*x)) / 2 - 2*x. G.f.: -2*x + 1 - x / (1 - x / (1 - x / ...)) (continued fraction). a(n) = A115140(n) = A115141(n) for all n in Z unless n=1. a(n) = -A000108(n-1) for all n>1. EXAMPLE G.f. = 1 - 3*x - x^2 - 2*x^3 - 5*x^4 - 14*x^5 - 42*x^6 - 132*x^7 - 429*x^8 + ... MATHEMATICA CoefficientList[Series[(1 +Sqrt[1-4*x])/2 -2*x, {x, 0, 50}], x] (* G. C. Greubel, Aug 04 2018 *) PROG (PARI) {a(n) = if( n<2, (n==0) - 3*(n==1), - binomial(2*n - 2, n-1) / n)}; (PARI) {a(n) = if( n<0, 0, polcoeff( (1 + sqrt(1 - 4*x + x * O(x^n))) / 2 - 2*x, n))}; (Magma) m:=50; R:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1 +Sqrt(1-4*x))/2 -2*x)); // G. C. Greubel, Aug 04 2018 CROSSREFS Cf. A000108, A001700, A115140, A115141. Sequence in context: A144204 A048226 A049919 * A112571 A051277 A300908 Adjacent sequences: A246429 A246430 A246431 * A246433 A246434 A246435 KEYWORD sign AUTHOR Michael Somos, Nov 14 2014 STATUS approved

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Last modified August 5 22:15 EDT 2024. Contains 374957 sequences. (Running on oeis4.)