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A107232 Expansion of (1+xc(x^2))^3/sqrt(1-4x^2), c(x) the g.f. of A000108. 1
1, 3, 5, 10, 18, 35, 65, 126, 238, 462, 882, 1716, 3300, 6435, 12441, 24310, 47190, 92378, 179894, 352716, 688636, 1352078, 2645370, 5200300, 10192588, 20058300, 39373700, 77558760, 152443080, 300540195, 591385545, 1166803110, 2298248550 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

An inverse Chebyshev transform of C(3,n)=(1,3,3,1,0,0,0,...), where g(x)->(1/sqrt(1-4x^2))g(xc(x^2)). In general, (1+xc(x^2))^r/sqrt(1-4x^2) has general term a(n)=sum{k=0..floor(n/2), binomial(n,k)*binomial(r,n-2k)}, r>0.

REFERENCES

Piera Manara and Claudio Perelli Cippo, The fine structure of 4321 avoiding involutions and 321 avoiding involutions, PU. M. A. Vol. 22 (2011), 227-238; http://www.mat.unisi.it/newsito/puma/public_html/22_2/manara_perelli-cippo.pdf. - From N. J. A. Sloane, Oct 13 2012

LINKS

Table of n, a(n) for n=0..32.

FORMULA

a(n)=sum{k=0..floor(n/2), binomial(n, k)*binomial(3, n-2k)}.

Conjecture: -(n+3)*(3*n-2)*a(n) +12*n*a(n-1) +4*(3*n+1)*(n-1)*a(n-2)=0. - R. J. Mathar, Jan 04 2017

CROSSREFS

Sequence in context: A094986 A154949 A318248 * A134522 A001445 A192860

Adjacent sequences:  A107229 A107230 A107231 * A107233 A107234 A107235

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 13 2005

STATUS

approved

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Last modified October 15 17:24 EDT 2019. Contains 328037 sequences. (Running on oeis4.)