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 A173895 E.g.f. satisfies: A'(x) = 1/(1 + x*A(x)) with A(0) = 1. 3
 1, 1, -1, 0, 9, -48, 15, 2448, -24927, 23424, 3091311, -47659200, 88056969, 10702667520, -225139993377, 679791291648, 78646340795265, -2128005345251328, 9456106738649631, 1053535684549174272 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Define a polynomial sequence P_n(x) recursively by ... P_0(x) = 1, and for n >= 1 ... P_n(x) = (x-1)*P_(n-1)(x-1)-n*P_(n-1)(x+1). The first few polynomials are P_1(x) = x-2 P_2(x) = x^2-6*x+5 P_3(x) = x^3-12*x^2+32*x-12. It appears that a(n+1) = P_n(1) (checked as far as a(19)). Compare with A144010. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..190 FORMULA E.g.f. satisfies: A(x) = 1 + Integral 1/(1 + x*A(x)) dx. E.g.f. satisfies: A(G(x)) = 1 + x where G(x) is the e.g.f. of A000932 (offset 1). [Paul D. Hanna, Aug 23 2011] EXAMPLE E.g.f.: A(x) = 1 + x - x^2/2! + 9*x^4/4! - 48*x^5/5! + 15*x^6/6! + 2448*x^7/7! +... where 1/(1 + x*A(x)) = 1 - x + 9*x^3/3! - 48*x^4/4! + 15*x^5/5! + 2448*x^6/6! +... Also, A(G(x)) = 1 + x where G(x) = x + x^2/2! + 3*x^3/3! + 6*x^4/4! + 18*x^5/5! + 48*x^6/6! + 156*x^7/7! + 492*x^8/8! +...+ A000932(n-1)*x^n/n! +... MATHEMATICA m = 20; A[_] = 1; Do[A[x_] = 1 + Integrate[1/(1+x*A[x])+O[x]^m, x]+O[x]^m // Normal, {m}]; CoefficientList[A[x], x] * Range[0, m-1]! (* Jean-François Alcover, Nov 02 2019 *) PROG (PARI) {a(n)=local(A=1+x); for(i=0, n, A=1+intformal(1/(1+x*A+x*O(x^n)) )); n!*polcoeff(A, n)} CROSSREFS Cf. A144010, A000932. Sequence in context: A207318 A293042 A159525 * A286437 A212107 A073979 Adjacent sequences:  A173892 A173893 A173894 * A173896 A173897 A173898 KEYWORD easy,sign AUTHOR Peter Bala, Nov 26 2010 STATUS approved

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Last modified February 28 23:19 EST 2020. Contains 332353 sequences. (Running on oeis4.)