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%I #31 Feb 11 2021 09:02:18
%S 1,1,2,4,12,32,104,304,1008,3072,10272,32064,107712,341504,1150592,
%T 3688192,12451584,40239104,136053248,442442752,1497664512,4894728192,
%U 16583583744,54419632128,184511361024,607524225024,2061074178048,6805625192448,23100352413696,76462341095424,259648659554304
%N a(n) = A100631(n, floor(n/2)).
%C "Middle" diagonal of _Reinhard Zumkeller_'s symmetric (Pascal-like) triangular array A100631.
%F a(n) = A100631(n, floor(n/2)) = A100631(n, ceiling(n/2)).
%F a(2*n) = A152254(n-1) = 2*A084773(n-1) for n >= 1.
%F 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
%o (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
%Y Cf. A084773, A100631, A152254.
%K nonn
%O 0,3
%A _Petros Hadjicostas_, Feb 09 2021
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