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A051256
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Numbers formed from binomial coefficients (mod 2) interpreted as digits in factorial base.
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3
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1, 3, 7, 33, 121, 843, 5167, 46233, 362881, 3991683, 40279687, 522910113, 6227383801, 93409304523, 1313941673647, 22324392524313, 355687428096001, 6758061133824003, 122000787836928007, 2561305169719296033
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (k+1)!(C(n, k) mod 2).
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EXAMPLE
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a(5) = 1! + 2! + 5! + 6! = 843 (only the first, second, fifth and sixth terms are odd in row 5 of Pascal's Triangle).
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MAPLE
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A051256(n) := proc(n) local i; RETURN(add(((binomial(n, i) mod 2)*((i+1)!)), i=0..n)); end;
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MATHEMATICA
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Table[Sum[(k+1)!Mod[Binomial[n, k], 2], {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Feb 14 2013 *)
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PROG
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(Python)
from math import factorial
return sum(0 if ~n & k else factorial(k+1) for k in range(n+1)) # Chai Wah Wu, Feb 08 2016
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CROSSREFS
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KEYWORD
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nonn,nice,base
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AUTHOR
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STATUS
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approved
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