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A073389
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Second convolution of A002605(n) (generalized (2,2)-Fibonacci), n >= 0, with itself.
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7
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1, 6, 30, 128, 504, 1872, 6672, 23040, 77616, 256288, 832416, 2666496, 8441600, 26454528, 82174464, 253280256, 775316736, 2358812160, 7137023488, 21487386624, 64401106944, 192229535744, 571630694400, 1693996941312, 5004131659776, 14738997288960, 43293528760320
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} b(k)*c(n-k) with b(k) = A002605(k) and c(k) = A073388(k).
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+2, 2)*binomial(n-k, k)*2^(n-k).
a(n) = (n+3)*((n+1)*U(n+1) + (n+2)*U(n))/12, with U(n) = A002605(n), n >= 0.
G.f.: 1/(1-2*x*(1+x))^3.
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MATHEMATICA
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CoefficientList[Series[1/(1-2x(1+x))^3, {x, 0, 25}], x] (* Harvey P. Dale, Mar 14 2011 *)
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PROG
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(GAP) List([0..25], n->2^n*Sum([0..Int(n/2)], k->Binomial(n-k+2, 2)*Binomial(n-k, k)*(1/2)^k)); # Muniru A Asiru, Jun 12 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-2*x-2*x^2)^3 )); // G. C. Greubel, Oct 03 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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