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 A179200 E.g.f. equals the real part of the i-th iteration of (x + x^2), where i=sqrt(-1). 2
 0, 1, 0, -6, 60, -600, 5880, -38640, -624960, 45077760, -1773129600, 58531809600, -1657462435200, 33703750080000, 171919752076800, -76383384045696000, 6034124486347776000, -348318907415331840000, 15862493882862941184000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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 G(x) = e.g.f. of A179201 and F(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.: F(x) satisfies: . F(x) = (G(x+x^2)/G(x) - 1)/2 . G(x) = sqrt( F(x) + F(x)^2 - F(x+x^2) ) where G(x) is the e.g.f. of A179201. EXAMPLE E.g.f: F(x) = x - 6*x^3/3! + 60*x^4/4! - 600*x^5/5! + 5880*x^6/6! +... The e.g.f. of A179201, G(x), begins: G(x) = 2*x^2/2! - 6*x^3/3! + 12*x^4/4! + 200*x^5/5! - 6240*x^6/6! + 139440*x^7/7! - 2869440*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, real(n!*N[n, 1]))} CROSSREFS Cf. A179201, A030528. Sequence in context: A122653 A299869 A136943 * A136938 A136930 A136936 Adjacent sequences: A179197 A179198 A179199 * A179201 A179202 A179203 KEYWORD sign AUTHOR Paul D. Hanna, Jul 02 2010 STATUS approved

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Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)