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 A159315 E.g.f. satisfies: d/dx log(A(x)) = A(2*x)^(1/2). 4
 1, 1, 2, 7, 41, 406, 7127, 235147, 15191966, 1953128401, 501361942127, 257110692345262, 263513099974512041, 539923433830720468321, 2212048542930121133510402, 18123271334339868892408048927 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row 0 of array A159314. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..78 FORMULA E.g.f. satisfies: A'(x) = A(x)*A(2*x)^(1/2). a(n) = Sum_{i=0..n-1} C(n-1,i)*A126444(i)*a(n-1-i) for n>0 with a(0)=1. E.g.f.: A(x) = G(x/2)^2 where G(x) = e.g.f. of A126444. E.g.f.: A(x) = F(x/4)^4 where F(x) = e.g.f. of A159316. a(n) ~ c * 2^(n*(n-3)/2), where c = 14.6416352593041803546... - Vaclav Kotesovec, Feb 23 2014 EXAMPLE E.g.f.: A(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 41*x^4/4! + 406*x^5/5! +... Related expansions: log(A(x)) = x +x^2/2! +3*x^3/3! +19*x^4/4! +225*x^5/5! +4801*x^6/6! +... A(2*x)^(1/2) = 1 + x + 3*x^2/2! +19*x^3/3! +225*x^4/4! +4801*x^5/5! +... in which the coefficients are given by A126444. PROG (PARI) {a(n)=local(A=vector(n+2, j, 1+j*x)); for(i=0, n+1, for(j=0, n, m=n+1-j; A[m]=exp(intformal((A[m+1]+x*O(x^n))^(2^(m-1)))))); n!*polcoeff(A[1], n, x)} CROSSREFS Cf. A159314, A126444, A159316, A159317. Sequence in context: A008934 A084871 A122942 * A191601 A265772 A109172 Adjacent sequences:  A159312 A159313 A159314 * A159316 A159317 A159318 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 19 2009 STATUS approved

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Last modified May 26 14:52 EDT 2020. Contains 334626 sequences. (Running on oeis4.)