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A134759
a(n) = 2*A000984(n) - (n+1).
5
1, 2, 9, 36, 135, 498, 1841, 6856, 25731, 97230, 369501, 1410852, 5408299, 20801186, 80233185, 310235024, 1202160763, 4667212422, 18150270581, 70690527580, 275693057619, 1076515748858, 4208197927417, 16466861455176, 64495207366175, 252821212875478
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, May 28 2024: (Start)
a(n) = (n+1)*(2*A000108(n) - 1).
a(n) = (2*(2*n-1)*a(n-1) + 3*n*(n-1))/n.
G.f.: 2/sqrt(1-4*x) - 1/(1-x)^2.
E.g.f.: 2*exp(2*x)*BesselI(0, 2*x) - (1+x)*exp(x). (End)
MATHEMATICA
Table[2 Binomial[2n, n]-n-1, {n, 0, 30}] (* Harvey P. Dale, Aug 07 2023 *)
PROG
(Magma) [(n+1)*(2*Catalan(n)-1): n in [0..40]]; // G. C. Greubel, May 28 2024
(SageMath) [2*binomial(2*n, n) -(n+1) for n in range(41)] # G. C. Greubel, May 28 2024
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Nov 09 2007
EXTENSIONS
More terms from Harvey P. Dale, Aug 07 2023
STATUS
approved