A104688 Binomial transform of Moebius sequence.
1, 0, -2, -5, -10, -18, -30, -48, -77, -127, -213, -351, -551, -817, -1181, -1819, -3304, -7003, -15454, -32185, -59830, -94733, -116204, -70931, 138782, 634477, 1440741, 2129014, 995270, -6559829, -30802323, -91672920, -223074852, -473661244, -893720326, -1483495634, -2049478628
Offset: 1
Keywords
Examples
G.f.: A(x) = x - 2*x^3 - 5*x^4 - 10*x^5 - 18*x^6 - 30*x^7 - 48*x^8 - 77*x^9 - 127*x^10 - 213*x^11 - 351*x^12 + ...
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 1..1000
- N. J. A. Sloane, Transforms
Programs
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Mathematica
Table[Sum[Binomial[n-1, k-1]*MoebiusMu[k], {k, 1, n}], {n, 1, 50}] (* Vaclav Kotesovec, Jun 01 2025 *)
Formula
G.f. A(x) satisfies x = Sum_{n>=1} A( x^n/(1 + x^n) ). - Paul D. Hanna, Jun 03 2025