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 A143918 G.f. A(x) satisfies: A(x) = 1/(1-x)^2 + x^2*A'(x). 1
 1, 2, 5, 14, 47, 194, 977, 5870, 41099, 328802, 2959229, 29592302, 325515335, 3906184034, 50780392457, 710925494414, 10663882416227, 170622118659650, 2900576017214069, 52210368309853262, 991996997887211999, 19839939957744240002, 416638739112629040065 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..450 FORMULA a(n) = 3*floor(e*(n-1)!) - 1, n>1. - Gary Detlefs, Jun 10 2010 EXAMPLE G.f.: A(x) = 1 + 2*x + 5*x^2 + 14*x^3 + 47*x^4 + 194*x^5 + 977*x^6 +... x^2*A'(x) = 2*x^2 + 10*x^3 + 42*x^4 + 188*x^5 + 970*x^6 + 5862*x^7 +... MAPLE a:= proc(n) option remember; `if`(n<3, n^2+1,       ((n^2+1)*a(n-1)-(n-2)*(n+1)*a(n-2))/n)     end: seq(a(n), n=0..25);  # Alois P. Heinz, Jul 16 2017 MATHEMATICA a=2; lst={}; Do[a=n+a*(n-2); AppendTo[lst, a], {n, 0, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 16 2010 *) PROG (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x+x*O(x^n))^2+x^2*deriv(A)); polcoeff(A, n)} CROSSREFS Sequence in context: A007268 A326898 A109156 * A129867 A119841 A149905 Adjacent sequences:  A143915 A143916 A143917 * A143919 A143920 A143921 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 05 2008 STATUS approved

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Last modified May 26 14:46 EDT 2020. Contains 334626 sequences. (Running on oeis4.)