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Beginning of a polynomial relation of degree n in n+2 terms in the first half of Pascal's triangle. See A241201.
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%I #4 Apr 22 2014 10:50:21

%S 1,2,26,9,149,489

%N Beginning of a polynomial relation of degree n in n+2 terms in the first half of Pascal's triangle. See A241201.

%C Is this sequence finite?

%t t = Table[k = 1; While[b = Binomial[k, Range[0, k/2]]; d = Differences[b, n + 1]; ! MemberQ[d, 0], k++]; {k, Position[d, 0, 1, 1][[1, 1]] - 1}, {n, 6}]; Transpose[t][[2]]

%Y Cf. A008865 (binomial(n,k) has 3 consecutive terms in a linear relation).

%Y Cf. A062730 (3 terms in arithmetic progression in Pascal's triangle).

%Y Cf. A241199, A241200 (similar, but quadratic).

%K nonn,more

%O 1,2

%A _T. D. Noe_, Apr 21 2014