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A341344
a(n) = A100631(n, floor(n/2)).
1
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
0,3
COMMENTS
"Middle" diagonal of Reinhard Zumkeller's symmetric (Pascal-like) triangular array A100631.
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
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Petros Hadjicostas, Feb 09 2021
STATUS
approved