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 A179201 E.g.f. equals the imaginary part of the i-th iteration of (x + x^2), where i=sqrt(-1). 2
 0, 0, 2, -6, 12, 200, -6240, 139440, -2869440, 53386560, -708048000, -6667689600, 1162101600000, -68789252563200, 3158414682259200, -118988867559744000, 3123174474201600000, 17680394964750336000, -10490102782572441600000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Let H(x) equal the i-th iteration of (x + x^2), then . the inverse of H(x) equals the conjugate of H(x); . H(x+x^2) = H(x) + H(x)^2; . H(x) = F(x) + i*G(x) where F(x) = e.g.f. of A179200 and G(x) = e.g.f. of this sequence, where H(F(x) - i*G(x)) = x; . coefficients of H(x) form the first column of triangular matrix A030528 raised to the i-th power, where A030528(n,k) = C(k,n-k). LINKS FORMULA E.g.f.: G(x) satisfies: . G(x) = sqrt( F(x) + F(x)^2 - F(x+x^2) ) . F(x) = (G(x+x^2)/G(x) - 1)/2 where F(x) is the e.g.f. of A179200. EXAMPLE E.g.f: G(x) = 2*x^2/2! - 6*x^3/3! + 12*x^4/4! + 200*x^5/5! +... The e.g.f. of A179200, F(x), begins: F(x) = x - 6*x^3/3! + 60*x^4/4! - 600*x^5/5! + 5880*x^6/6! - 38640*x^7/7! - 624960*x^8/8! +... The i-th iteration of (x + x^2) = H(x) = F(x) + i*G(x), begins: H(x) = x + i*x^2 - (1 + i)*x^3 + (5 + i)*x^4/2 - (15 - 5*i)*x^5/3 + (49 - 52*i)*x^6/6 - (23 - 83*i)*x^7/3 - (93 + 427*i)*x^8/6 + (15652 + 18537*i)*x^9/126 - (61567 + 24585*i)*x^10/126 + (369519 - 42094*i)*x^11/252 - (1743963 - 1222750*i)*x^12/504 + ... where H(F(x) - i*G(x)) = x. PROG (PARI) {a(n)=local(M=matrix(n+1, n+1, r, c, if(r>=c, binomial(c, r-c))), L=sum(k=1, #M, -(M^0-M)^k/k), N=sum(k=0, #L, (I*L)^k/k!)); if(n<1, 0, imag(n!*N[n, 1]))} CROSSREFS Cf. A179200, A030528. Sequence in context: A290406 A319481 A195338 * A105122 A132076 A309743 Adjacent sequences:  A179198 A179199 A179200 * A179202 A179203 A179204 KEYWORD sign AUTHOR Paul D. Hanna, Jul 02 2010 STATUS approved

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Last modified June 18 03:46 EDT 2021. Contains 345098 sequences. (Running on oeis4.)