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A116387
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Expansion of 1/(sqrt(1-2x-3x^2)(2-M(x))), where M(x) is the g.f. of the Motzkin numbers A001006.
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2
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1, 2, 7, 22, 72, 234, 763, 2486, 8099, 26372, 85833, 279226, 907946, 2951066, 9587981, 31140034, 101104048, 328162170, 1064856217, 3454513274, 11204337056, 36332719182, 117795920249, 381848062066, 1237615088203, 4010710218384
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A116383.
The substitution x-> x/(1+x+x^2) in the g.f. (this might be called an inverse Motzkin transform) yields the g.f. of A074331. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 10 2008]
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FORMULA
| a(n)=sum{k=0..n, sum{j=0..n, C(n,j-k)C(j,n-j)}}.
Conjecture: n*(17*n-142)*a(n) +(17*n^2+95*n+138)*a(n-1) +(-391*n^2+2488*n-2908)*a(n-2) +(-17*n^2-603*n+1892)*a(n-3) +2*(697*n-2021)*(n-4)*a(n-4) +60*(17*n-47)*(n-4)*a(n-5) = 0. - R. J. Mathar, Nov 15 2011
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MATHEMATICA
| Table[Sum[Binomial[n, j-k]Binomial[j, n-j], {k, 0, n}, {j, 0, n}], {n, 0, 30}] (* From Harvey P. Dale, Feb 08 2012 *)
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CROSSREFS
| Sequence in context: A092690 A030186 A162770 * A114495 A137398 A151439
Adjacent sequences: A116384 A116385 A116386 * A116388 A116389 A116390
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 12 2006
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