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Search: id:A159315
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| A159315 |
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E.g.f. satisifies: d/dx log(A(x)) = A(2*x)^(1/2). |
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+0
4
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| 1, 1, 2, 7, 41, 406, 7127, 235147, 15191966, 1953128401, 501361942127, 257110692345262, 263513099974512041, 539923433830720468321, 2212048542930121133510402, 18123271334339868892408048927
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row 0 of array A159314.
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FORMULA
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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.
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EXAMPLE
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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.
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PROGRAM
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(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)}
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CROSSREFS
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Cf. A159314, A126444, A159316, A159317.
Sequence in context: A008934 A084871 A122942 this_sequence A109172 A131682 A158840
Adjacent sequences: A159312 A159313 A159314 this_sequence A159316 A159317 A159318
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Apr 19 2009
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