login
Denominators of inverse unimodal analog of binomial coefficients: binomial(n,m) = Sum_{k=0..n-m} a(2*k+m-1, 2*k).
2

%I #9 Aug 26 2019 22:37:17

%S 1,1,1,1,2,1,1,8,1,1,1,16,1,2,1,1,128,1,8,1,1,1,256,1,16,1,2,1,1,1024,

%T 1,128,1,8,1,1,1,2048,1,256,1,16,1,2,1,1,32768,1,1024,1,128,1,8,1,1,1,

%U 65536,1,2048,1,256,1,16,1,2,1,1,262144,1,32768,1,1024,1,128,1,8,1,1

%N Denominators of inverse unimodal analog of binomial coefficients: binomial(n,m) = Sum_{k=0..n-m} a(2*k+m-1, 2*k).

%C Entries are powers of 2.

%H G. C. Greubel, <a href="/A072286/b072286.txt">Rows n = 0..100 of triangle, flattened</a>

%F a(n, m) = binomial(n-m/2+1, n-m+1) - binomial(n-m/2, n-m+1).

%t a[n_, m_]:= Binomial[n -m/2 +1, n-m+1] - Binomial[n -m/2, n-m+1]; Flatten[Table[Denominator[a[n, m]], {n, 0, 11}, {m, 0, n}]]

%o (PARI) a(n,m) = binomial(n-m/2, n-m);

%o for(n=0,11, for(m=0,n, print1(denominator(a(n,m)), ", "))) \\ _G. C. Greubel_, Aug 26 2019

%o (Sage) [[denominator( binomial(n-m/2, n-m) ) for m in (0..n)] for n in (0..11)] # _G. C. Greubel_, Aug 26 2019

%Y Cf. A072285, A071922.

%K nonn,easy,frac,tabl

%O 0,5

%A Michele Dondi (bik.mido(AT)tiscalinet.it), Jul 11 2002