A186335 A transform of the central binomial coefficients.

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

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