A072286 Denominators of inverse unimodal analog of binomial coefficients: binomial(n,m) = Sum_{k=0..n-m} a(2*k+m-1, 2*k).

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

Offset: 0

Author

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

Keywords

• nonn
• easy
• frac
• tabl

Comments

Entries are powers of 2.

Links

• G. C. Greubel, Rows n = 0..100 of triangle, flattened

Crossrefs

Cf. A072285, A071922.

Programs

Mathematica

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}]]

PARI

a(n,m) = binomial(n-m/2, n-m);
for(n=0,11, for(m=0,n, print1(denominator(a(n,m)), ", "))) \\ G. C. Greubel, Aug 26 2019

Sage

[[denominator( binomial(n-m/2, n-m) ) for m in (0..n)] for n in (0..11)] # G. C. Greubel, Aug 26 2019

Formula

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