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A156361
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a(2*n+2) = 7*a(2*n+1), a(2*n+1) = 7*a(2*n) - 6^n*A000108(n), a(0) = 1.
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5
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1, 6, 42, 288, 2016, 14040, 98280, 686880, 4808160, 33638976, 235472832, 1647983232, 11535882624, 80745019776, 565215138432, 3956385876480, 27694701135360, 193860506096640, 1357023542676480, 9499115800977408
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OFFSET
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0,2
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COMMENTS
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Hankel transform is 6^C(n+1, 2).
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LINKS
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FORMULA
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a(n) = Sum{k=0..n} A120730(n,k) * 6^k.
(n+1)*a(n) = 7*(n+1)*a(n-1) + 24*(n-2)*a(n-2) - 168*(n-2)*a(n-3). - R. J. Mathar, Jul 21 2016
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MAPLE
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option remember;
local nh;
if n= 0 then
1;
elif type(n, 'even') then
7*procname(n-1);
else
nh := floor(n/2) ;
end if;
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MATHEMATICA
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a[n_]:= a[n]= If[n==0, 1, 7*a[n-1] -If[EvenQ[n], 0, 6^((n-1)/2)* CatalanNumber[(n-1)/2]]];
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PROG
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(Magma) [n le 3 select Factorial(n+4)/120 else (7*n*Self(n-1) + 24*(n-3)*Self(n-2) - 168*(n-3)*Self(n-3))/n: n in [1..30]]; // G. C. Greubel, Nov 09 2022
(SageMath)
if (n==0): return 1
elif (n%2==1): return 7*a(n-1) - 6^((n-1)/2)*catalan_number((n-1)/2)
else: return 7*a(n-1)
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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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