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A325582
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G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n * ((1 + 2*x)^n - A(x))^(n+1), where A(0) = 0.
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5
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1, 3, 5, 35, 181, 1135, 8145, 61839, 509601, 4463439, 41334849, 402989487, 4117422337, 43944607807, 488583342657, 5645234756671, 67645819918849, 839125267708479, 10758054102964545, 142339717159997439, 1941001581534636545, 27246049579466191103, 393252398533473468673, 5830129052356606111743, 88696151815740778017537, 1383441162884970338467071, 22104519997332116663070721, 361513358284734334108704767
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f. A(x) satisfies:
(1) 1 = Sum_{n>=0} x^n * ((1 + 2*x)^n - A(x))^(n+1).
(2) 1 + x = Sum_{n>=0} x^n * (1 + 2*x)^(n*(n-1)) / (1 + x*(1 + 2*x)^n*A(x))^(n+1).
FORMULA FOR TERMS.
a(n) = 1 (mod 2) for n >= 0.
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EXAMPLE
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G.f.: A(x) = x + 3*x^2 + 5*x^3 + 35*x^4 + 181*x^5 + 1135*x^6 + 8145*x^7 + 61839*x^8 + 509601*x^9 + 4463439*x^10 + 41334849*x^11 + 402989487*x^12 + ...
such that
1 = (1 - A(x)) + x*((1+2*x) - A(x))^2 + x^2*((1+2*x)^2 - A(x))^3 + x^3*((1+2*x)^3 - A(x))^4 + x^4*((1+2*x)^4 - A(x))^5 + x^5*((1+2*x)^5 - A(x))^6 + x^6*((1+2*x)^6 - A(x))^7 + ...
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PROG
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(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); A[#A] = polcoeff( sum(m=0, #A, x^m*((1 + 2*x +x*O(x^#A))^m - x*Ser(A))^(m+1) ), #A); ); A[n+1]}
for(n=0, 30, print1(a(n), ", "))
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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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