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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 G. C. Greubel, Table of n, a(n) for n = 0..1000 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 Cf. A000108, A000984, A134771. Sequence in context: A026329 A014533 A255453 * A272787 A084780 A268202 Adjacent sequences: A134767 A134768 A134769 * A134771 A134772 A134773 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.)