A390686 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(3*n-2*k,n-2*k).

1, 3, 14, 77, 451, 2728, 16834, 105317, 665551, 4238463, 27156744, 174858972, 1130494236, 7333934988, 47717158394, 311248100517, 2034664811631, 13326556644753, 87435235471214, 574537592170357, 3780472550923091, 24906432444097408, 164272522873515704

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) = [x^n] 1/((1+x^2) * (1-x)^(2*n+1)).

a(n) = Sum_{k=0..n} (-2)^k * binomial(3*n+k+2,n-k).

Prog

(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(3*n-2*k, n-2*k));

Crossrefs

Cf. A176332, A390687.

Sequence in context: A198649 A198656 A240402 * A394120 A048779 A369477

Adjacent sequences: A390683 A390684 A390685 * A390687 A390688 A390689

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2025

Status

approved