A006987 Binomial coefficients: C(n,k), 2 <= k <= n-2, sorted, duplicates removed. (Formerly M4084)

6, 10, 15, 20, 21, 28, 35, 36, 45, 55, 56, 66, 70, 78, 84, 91, 105, 120, 126, 136, 153, 165, 171, 190, 210, 220, 231, 252, 253, 276, 286, 300, 325, 330, 351, 364, 378, 406, 435, 455, 462, 465, 495, 496, 528, 560, 561, 595, 630, 666, 680, 703, 715, 741, 780, 792, 816, 820

Offset

1,1

Comments

Complement of A137905; a(n) > A058084(a(n)). - Reinhard Zumkeller, Mar 20 2009

Or numbers l which, for the first time, appear in m-th row of the Pascal triangle for m < l. - Vladimir Shevelev, Apr 28 2010

Appears to be the set of simplex numbers of order > 2 and dimension > 1. - Dylan Hamilton, Nov 05 2010

This is correct (assuming the notational choice of giving the first n-simplicial number index 1), as the n-th diagonal or antidiagonal of Pascal's triangle gives the n-simplicial numbers. - Thomas Anton, Dec 04 2018

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

R. G. Wilson v, Letter to N. J. A. Sloane, Nov. 1988

R. G. Wilson v, Letter to N. J. A. Sloane, Jan. 1989

Example

Pascal's triangle (A007318) with the outer two layers removed:
             6
          10  10
        15  20  15
      21  35  35  21
    28  56  70  56  28
  36  84 126 126  84  36
  ...

Mathematica

Take[ Union[ Flatten[ Table[ Binomial[n, k], {n, 2, 45}, {k, 2, n - 2}]]], 58] (* Robert G. Wilson v, May 25 2004 *)

Prog

(PARI) list(lim)=my(v=List(), t); for(n=4, sqrtint(2*lim)+1, for(k=2, n\2, t=binomial(n, k); if(t>lim, break, listput(v, t)))); vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Apr 03 2012

Crossrefs

Cf. A002808, A007318.

Sequence in context: A315248 A315249 A319382 * A182237 A337612 A315250

Adjacent sequences: A006984 A006985 A006986 * A006988 A006989 A006990

Keyword

nonn

Author

N. J. A. Sloane, Robert G. Wilson v

Extensions

More terms from David W. Wilson

Spelling corrected by Jason G. Wurtzel, Aug 22 2010

Status

approved