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A134770 a(n) = 4*A000984(n) - 3. 2
1, 5, 21, 77, 277, 1005, 3693, 13725, 51477, 194477, 739021, 2821725, 10816621, 41602397, 160466397, 620470077, 2404321557, 9334424877, 36300541197, 141381055197, 551386115277, 2153031497757, 8416395854877, 32933722910397, 128990414732397, 505642425751005, 1983674131792413 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The second inverse binomial transform of this sequence is A134771, the sequence interleaved with threes: (1, 3, 5, 3, 21, 3, 77, 3, ...).
LINKS
FORMULA
From G. C. Greubel, Oct 13 2023: (Start)
a(n) = 4*(n+1)*A000108(n) - 3.
G.f.: 4/sqrt(1-4*x) - 3/(1-x).
Sum_{n>=0} a(n)*x^(2*n)/(2*n)! = 4*BesselI(0, 2*x) - cosh(x). (End)
EXAMPLE
a(2) = 21 = 4*A000984(2) - 3 = 4*6 - 3.
MATHEMATICA
Table[4 Binomial[2n, n]-3, {n, 0, 30}] (* Harvey P. Dale, Dec 01 2022 *)
PROG
(PARI) a(n)=4*binomial(2*n, n) - 3; \\ Michel Marcus, Jul 02 2020
(Magma) [4*(n+1)*Catalan(n)-3: n in [0..40]]; // G. C. Greubel, Oct 13 2023
(SageMath) [4*binomial(2*n, n)-3 for n in range(41)] # G. C. Greubel, Oct 13 2023
CROSSREFS
Sequence in context: A026329 A014533 A255453 * A272787 A084780 A268202
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Nov 10 2007
EXTENSIONS
a(10) corrected and offsets aligned by Georg Fischer, Jul 01 2020
More terms from Michel Marcus, Jul 02 2020
STATUS
approved

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Last modified April 23 23:26 EDT 2024. Contains 371917 sequences. (Running on oeis4.)