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

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

Author

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

Keywords

• nonn

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

Examples

			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
  ...
		

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

Crossrefs

Cf. A002808, A007318.

Programs

Mathematica

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

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

Extensions

More terms from David W. Wilson

Spelling corrected by Jason G. Wurtzel, Aug 22 2010