A072285 Numerators 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, 3, 1, 1, 15, 2, 1, 1, 35, 3, 5, 1, 1, 315, 4, 35, 3, 1, 1, 693, 5, 105, 6, 7, 1, 1, 3003, 6, 1155, 10, 63, 4, 1, 1, 6435, 7, 3003, 15, 231, 10, 9, 1, 1, 109395, 8, 15015, 21, 3003, 20, 99, 5, 1, 1, 230945, 9, 36465, 28, 9009, 35, 429, 15, 11, 1

Offset: 0

Author

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

Keywords

• nonn
• easy
• frac
• tabl

Links

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

Crossrefs

Cf. A072286, A071922.

Programs

Mathematica

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

PARI

a(n,m) = binomial(n-m/2, n-m);
for(n=0,10, for(m=0,n, print1(numerator(a(n,m)), ", "))) \\ G. C. Greubel, Aug 26 2019

Sage

[[numerator( 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).