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A073389 Second convolution of A002605(n) (generalized (2,2)-Fibonacci), n >= 0, with itself. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
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.
MATHEMATICA
CoefficientList[Series[1/(1-2x(1+x))^3, {x, 0, 25}], x] (* Harvey P. Dale, Mar 14 2011 *)
PROG
(Sage) taylor( 1/(1-2*x-2*x^2)^3, x, 0, 25).list() # Zerinvary Lajos, Jun 03 2009; modified by G. C. Greubel, Oct 03 2022
(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
CROSSREFS
Third (m=2) column of triangle A073387, A073388.
Cf. A002605.
Sequence in context: A032205 A007465 A261389 * A320744 A232061 A247386
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 02 2002
STATUS
approved

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Last modified March 29 22:15 EDT 2024. Contains 371282 sequences. (Running on oeis4.)