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A090366
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Shifts 1 place left under the INVERT transform of the BINOMIAL transform of the self-convolution of this sequence.
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3
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1, 1, 4, 21, 131, 917, 6988, 56965, 491240, 4447558, 42048457, 413473928, 4215959294, 44469487070, 484303175837, 5437300482651, 62848069403649, 747063566345320, 9123406697372938, 114370704441951620, 1470590692488141315, 19381056189738194070
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: A(x) = 1/(1 - A(x/(1-x))^2*x/(1-x) ).
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MAPLE
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bintr:= proc(p) local b; b:= proc(n) option remember;
add(p(k) *binomial(n, k), k=0..n) end
end:
invtr:= proc(p) local b; b:= proc(n) option remember;
`if`(n<1, 1, add(b(n-i) *p(i-1), i=1..n+1)) end
end:
b:= invtr(bintr(n-> add(a(i)*a(n-i), i=0..n))):
a:= n-> `if`(n<0, 0, b(n-1)):
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MATHEMATICA
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m = 30; A[_] = 1; Do[A[x_] = 1/(1 - A[x/(1-x)]^2*(x/(1-x))) + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Jun 04 2018 *)
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PROG
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(PARI) {a(n)=local(A); if(n<0, 0, A=1+x+x*O(x^n); for(k=1, n, B=subst(A^2, x, x/(1-x))/(1-x)+x*O(x^n); A=1+x*A*B); polcoeff(A, n, x))}
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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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