A324568 a(n) = Sum_{i=0..n, j=0..n} (binomial(2*i, j) + binomial(2*j, i)).

2, 8, 32, 124, 482, 1882, 7380, 29036, 114530, 452638, 1791638, 7100430, 28167986, 111837902, 444351292, 1766536044, 7026526226, 27960911422, 111308958942, 443258277254, 1765690504666, 7035402933402, 28039342445582, 111773962249054, 445654589001882

Offset

0,1

Links

Table of n, a(n) for n=0..24.

Formula

Recurrence: 2*(n+1)*(5*n^2 - 21*n + 20)*a(n) = (85*n^3 - 332*n^2 + 243*n + 100)*a(n-1) - 3*(65*n^3 - 298*n^2 + 377*n - 100)*a(n-2) + 2*(20*n^3 - 109*n^2 + 191*n - 100)*a(n-3) + 8*(2*n - 5)*(5*n^2 - 11*n + 4)*a(n-4).

a(n) ~ 4^(n+1)/3 * (1 + 5/(3*sqrt(Pi*n))).

Mathematica

Table[Sum[Binomial[2*i, j] + Binomial[2*j, i], {i, 0, n}, {j, 0, n}], {n, 0, 30}]

Crossrefs

Cf. A000984, A006134, A007685, A324566, A324567.

Sequence in context: A282879 A217665 A337863 * A320654 A333579 A274524

Adjacent sequences: A324565 A324566 A324567 * A324569 A324570 A324571

Keyword

nonn

Author

Vaclav Kotesovec, Mar 07 2019

Status

approved