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A037965 a(n) = n*binomial(2*n-2, n-1). 11
0, 1, 4, 18, 80, 350, 1512, 6468, 27456, 115830, 486200, 2032316, 8465184, 35154028, 145608400, 601749000, 2481880320, 10218366630, 42004911960, 172427570700, 706905276000, 2894777105220, 11841673237680 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n+1) is the convolution of A000984 and A081294. - Paul Barry, Sep 18 2008

REFERENCES

The right-hand side of a binomial coefficient identity in H. W. Gould, Combinatorial Identities, Morgantown, 1972.

LINKS

Table of n, a(n) for n=0..22.

FORMULA

Starting (1, 4, 18, 80, ...), = binomial transform of A134757: (1, 3, 11, 37, 123, 401, ...); and double binomial transform of A100071 starting (1, 2, 6, 12, 30, ...). - Gary W. Adamson, Nov 08 2007

G.f.: F(1/2,2;1;4x). - Paul Barry, Sep 03 2008

From Paul Barry, Sep 18 2008: (Start)

G.f.: x(1-2x)/(1-4x)^(3/2);

a(n+1) = Sum_{k=0..n} C(2k,k)*(4^(n-k) + 0^(n-k))/2. (End)

Conjecture: (-n+1)*a(n) + 2*(3*n-4)*a(n-1) + 4*(-2*n+5)*a(n-2) = 0. - R. J. Mathar, Nov 30 2012

E.g.f.: x*exp(2*x)*BesselI(0,2*x). - Ilya Gutkovskiy, Aug 22 2018

PROG

(PARI) a(n) = n*binomial(2*n-2, n-1); \\ Joerg Arndt, Sep 04 2017

CROSSREFS

Cf. A000984.

Cf. A100071, A134757.

Sequence in context: A112619 A196810 A177755 * A045902 A090017 A257390

Adjacent sequences:  A037962 A037963 A037964 * A037966 A037967 A037968

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Zerinvary Lajos, Oct 02 2007

STATUS

approved

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Last modified October 17 07:55 EDT 2019. Contains 328106 sequences. (Running on oeis4.)