A341344 a(n) = A100631(n, floor(n/2)).

1, 1, 2, 4, 12, 32, 104, 304, 1008, 3072, 10272, 32064, 107712, 341504, 1150592, 3688192, 12451584, 40239104, 136053248, 442442752, 1497664512, 4894728192, 16583583744, 54419632128, 184511361024, 607524225024, 2061074178048, 6805625192448, 23100352413696, 76462341095424, 259648659554304

Offset: 0

Author

Petros Hadjicostas, Feb 09 2021

Keywords

• nonn

Comments

"Middle" diagonal of Reinhard Zumkeller's symmetric (Pascal-like) triangular array A100631.

Crossrefs

Cf. A084773, A100631, A152254.

Programs

PARI

a(n) = {my(m=matrix(n+1, n+1)); for (i=1, n+1, for (j=1, n+1, if ((j==1) || (j==i), m[i, j] = 1, if (j<=n, m[i,j] = 2*(if (i>1, m[i-1,j-1] + m[i-1,j], 0) - if (i>2, m[i-2,j-1], 0) ))););); m[n+1, (n+2)\2];} \\ Michel Marcus, Feb 10 2021

Formula

a(n) = A100631(n, floor(n/2)) = A100631(n, ceiling(n/2)).

a(2*n) = A152254(n-1) = 2*A084773(n-1) for n >= 1.

a(n) = 2^ceiling(n/2)*hypergeom([-floor(n/2) + 1, ceiling(n/2)], [1], -1); see the comments for A100631. - Petros Hadjicostas, Feb 10 2021