A074801 a(n) is the sum of the n-th row of the triangle formed by replacing each m in Pascal's triangle with sigma(m).
1, 2, 5, 10, 28, 50, 116, 178, 528, 1282, 2794, 4778, 10594, 17166, 33426, 60242, 183072, 304202, 759716, 1288642, 2965286, 6352098, 11776586, 18326642, 48714362, 95769336, 172377654, 417138342, 1004225842, 1633822142, 3266821106, 4706920002, 16520601024
Offset: 0
Examples
The third row of Pascal's triangle is 1 3 3 1. When each n here is replaced by sigma(n), the row becomes 1 4 4 1 with a sum of 10, so a(3) = 10.
Links
- Robert G. Wilson v, Table of n, a(n) for n = 0..3000
Programs
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Mathematica
a[n_] := Sum[DivisorSigma[1, Binomial[n, i]], {i, 0, n}]; Table[a[i], {i, 1, 21}] -
PARI
a(n) = sum(k=0, n, sigma(binomial(n, k))); \\ Michel Marcus, Mar 17 2017
Formula
a(n) >= 2^n with equality for n <= 2. - Michel Marcus, Mar 19 2017
Extensions
More terms from Carl Najafi, Oct 10 2011
Offset changed to 0 by Editors, Mar 19 2017