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T(n, k) = denominator([x^n] N(1/2, n, x)) where N(a, n, x) is the n-th Nørlund polynomial.
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%I #8 Feb 18 2024 10:32:54

%S 1,4,1,48,2,1,64,16,4,1,1280,16,8,1,1,3072,256,32,24,4,1,86016,512,

%T 256,16,16,2,1,49152,12288,1024,256,64,16,4,1,2949120,6144,3072,384,

%U 128,8,12,1,1,1310720,327680,4096,1024,512,640,16,4,4,1,11534336,131072,65536,2048,2048,256,128,8,16,2,1

%N T(n, k) = denominator([x^n] N(1/2, n, x)) where N(a, n, x) is the n-th Nørlund polynomial.

%H Niels Erik Nørlund, <a href="http://www-gdz.sub.uni-goettingen.de/cgi-bin/digbib.cgi?PPN373206070">Vorlesungen über Differenzenrechnung</a>, Springer 1924.

%t Table[Denominator@CoefficientList[NorlundB[n, 1/2, x], x] , {n, 0, 10}] // Flatten

%Y Cf. A370414, A370416, A370417.

%K nonn,tabl,frac

%O 0,2

%A _Peter Luschny_, Feb 18 2024