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 A186335 A transform of the central binomial coefficients. 2
 1, 1, 4, 7, 21, 46, 127, 309, 832, 2131, 5709, 15010, 40281, 107423, 289314, 778087, 2103361, 5687938, 15427099, 41880357, 113912236, 310148223, 845598389, 2307657222, 6304306171, 17237338021, 47170965082, 129181447969, 354027263457, 970851960736, 2664008539017 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Hankel transform is (-1)^n*A128056(n). LINKS Table of n, a(n) for n=0..30. FORMULA a(n)=sum{k=0..n, sum{j=0..n, binomial(k-j,n-k-j)*binomial(k,j)*A000984(n-k-j)}}. Conjecture: n*a(n) +(-2*n+1)*a(n-1) +5*(-n+1)*a(n-2) +3*(2*n-3)*a(n-3) +5*(n-2)*a(n-4)=0. - R. J. Mathar, Feb 13 2015 a(n) ~ ((1+sqrt(21))/2)^(n + 3/2) / (2 * 21^(1/4) * sqrt(Pi*n)) . - Vaclav Kotesovec, Oct 30 2017 MAPLE A186335 := proc(n) add(add(binomial(k-j, n-k-j)*binomial(k, j)*A000984(n-k-j), j=0..n), k=0..n) ; end proc: # R. J. Mathar, Feb 13 2015 MATHEMATICA Table[Sum[Sum[Binomial[k-j, n-k-j]*Binomial[k, j]*Binomial[2*(n-k-j), n-k-j], {j, 0, n}], {k, 0, n}], {n, 0, 40}] (* Vaclav Kotesovec, Oct 30 2017 *) CROSSREFS Sequence in context: A255512 A039959 A320663 * A010363 A119561 A228015 Adjacent sequences: A186332 A186333 A186334 * A186336 A186337 A186338 KEYWORD nonn,easy AUTHOR Paul Barry, Feb 18 2011 STATUS approved

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Last modified August 6 02:44 EDT 2024. Contains 374957 sequences. (Running on oeis4.)