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A135867
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G.f. satisfies A(x) = 1 + x*A(2*x)^2.
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11
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1, 1, 4, 36, 640, 21888, 1451008, 188941312, 48768745472, 25069815595008, 25722272102744064, 52730972085034156032, 216091838647321476726784, 1770657164881170759078117376, 29013990909330956353981535748096
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OFFSET
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0,3
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COMMENTS
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Self-convolution equals A135868 such that 2^n*A135868(n) = a(n+1) for n >= 0.
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LINKS
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FORMULA
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a(n) = 2^(n-1)*Sum_{k=0..n-1} a(k)*a(n-k-1) for n>0 with a(0)=1. - Paul D. Hanna, Feb 09 2010
a(n) ~ c * 2^(n*(n+1)/2), where c = 0.715337433614869740944075474484711589980951273610257702786245519231799678... - Vaclav Kotesovec, Nov 04 2021
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MATHEMATICA
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nmax = 15; A[_] = 0; Do[A[x_] = 1 + x*A[2*x]^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* Vaclav Kotesovec, Nov 04 2021 *)
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PROG
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*subst(A, x, 2*x)^2); polcoeff(A, n)}
(PARI) a(n)=if(n==0, 1, 2^(n-1)*sum(k=0, n-1, a(k)*a(n-k-1))) \\ Paul D. Hanna, Feb 09 2010
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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