A100735 Inverse modulo 2 binomial transform of 2^n.
1, 1, 3, 3, 15, 15, 45, 45, 255, 255, 765, 765, 3825, 3825, 11475, 11475, 65535, 65535, 196605, 196605, 983025, 983025, 2949075, 2949075, 16711425, 16711425, 50134275, 50134275, 250671375, 250671375, 752014125, 752014125, 4294967295, 4294967295
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Thomas Baruchel, A non-symmetric divide-and-conquer recursive formula for the convolution of polynomials and power series, arXiv:1912.00452 [math.NT], 2019.
Programs
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Mathematica
Table[Sum[(-1)^ThueMorse[n - k]*Mod[Binomial[n, k], 2]*2^k, {k, 0, n}], {n, 0, 50}] (* G. C. Greubel, Apr 17 2018 *) -
PARI
for(n=0,50, print1(abs(sum(k=0,n,(-1)^(hammingweight(k)%2)* lift(Mod(binomial(n,k),2))*2^k)), ", ")) \\ G. C. Greubel, Apr 17 2018
Formula
a(n) = Sum_{k=0..n} (-1)^A010060(n-k)*mod(binomial(n, k), 2)*2^k.
Comments