id:A086618 - OEIS Search Results

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Main diagonal of square table A086617 of coefficients, T(n,k), of x^n*y^k in f(x,y) that satisfies f(x,y) = 1/[(1-x)(1-y)] + xy*f(x,y)^2.

+0
3

1, 2, 7, 33, 183, 1118, 7281, 49626, 349999, 2535078, 18758265, 141254655, 1079364105, 8350678170, 65298467487, 515349097713, 4100346740511, 32858696386766, 265001681344569 (list; graph; listen)

	OFFSET	`0,2`
	FORMULA	`a(n) = sum(k=0, n, A000108(k)*C(n, k)^2 ) where A000108(n)=Catalan(n)=(2n)!/(n!(n+1)!) and C(n, k)=n!/(k!(n-k)!). (From Michael Somos)`
	EXAMPLE	`a(5)= 1118 = 11^2 + 15^2 + 210^2 + 510^2 + 145^2 + 421^2.`
	CROSSREFS	`Cf. A086617 (table), A086615 (antidiagonal sums), A003046 (determinants).` `Cf. A000108.` `Sequence in context: A080119 A055724 A054727 this_sequence A104981 A058797 A121967` `Adjacent sequences: A086615 A086616 A086617 this_sequence A086619 A086620 A086621`
	KEYWORD	`nonn`
	AUTHOR	`Paul D. Hanna (pauldhanna(AT)juno.com), Jul 24 2003`

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Last modified September 8 08:06 EDT 2008. Contains 143486 sequences.

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