A011851 -id:A011851 - cp's OEIS frontend

A011857 Triangle of numbers [ C(n,k)/k ], k=1..n-1.

2, 3, 1, 4, 3, 1, 5, 5, 3, 1, 6, 7, 6, 3, 1, 7, 10, 11, 8, 4, 1, 8, 14, 18, 17, 11, 4, 1, 9, 18, 28, 31, 25, 14, 5, 1, 10, 22, 40, 52, 50, 35, 17, 5, 1, 11, 27, 55, 82, 92, 77, 47, 20, 6, 1, 12, 33, 73, 123, 158, 154, 113, 61, 24, 6, 1, 13, 39, 95, 178, 257, 286, 245, 160

Offset: 2

N. J. A. Sloane

Columns include A011848, A011849, A011850, A011851, A011852, A011853, A011854, A011855, A011856. Row sums are in A101687. Cf. A011847.

Flatten[Table[Floor[Binomial[n,k]/k],{n,20},{k,n-1}]] (* Harvey P. Dale, Apr 19 2015 *)

A215052 a(n) = (binomial(n,5) - floor(n/5)) / 5.

Original entry on oeis.org

1, 4, 11, 25, 50, 92, 158, 257, 400, 600, 873, 1237, 1713, 2325, 3100, 4069, 5266, 6729, 8500, 10625, 13155, 16145, 19655, 23750, 28500, 33981, 40274, 47466, 55650, 64925, 75397, 87178, 100387, 115150, 131600, 149878, 170132, 192518, 217200

Offset: 6

Peter Bala, Aug 01 2012

Apparently a duplicate of A036837. - R. J. Mathar, Aug 06 2012
Not the same as A011851.
Let p be a prime. Saikia and Vogrinc have proved that (1/p)*{binomial(n,p) - floor(n/p)} is an integer sequence. The present sequence is the case p = 5. Other cases are A002620 (p = 2), A014125 (p = 3), A215053 (p = 7) and A215054 (p = 11).
There is a connection between these sequences and A178904. For a fixed prime p the o.g.f. for the sequence (1/p)*{binomial(n,p) - floor(n/p)} is a rational function of the form x^(p+1)*R(p,x)/((1-x^p)*(1-x)^p). The polynomial R(p,x) = sum {k = 0..p-1} (1/p)*{1 - (-1)^k*binomial(p-1,k)}*x^(k-1). For prime p >= 3, -R(p,x) is equal to the p-th row polynomial of A178904.

M. P. Saikia and J. Vogrinc, A simple number theoretic result. (arxiv.1207.6707v1 [mathNT]), J. Assam Academy of Mathematics, Vol. 3, 90-96, 2010.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,2,-5,10,-10,5,-1).

Cf. A002620 (p = 2), A014125 (p = 3), A178904, A215053 (p = 7), A215054( p = 11).

a(n) = (1/5)*{binomial(n,5) - floor(n/5)}.

O.g.f.: sum {n>=0} a(n)*x^n = x^6*(1-x+x^2)/((1-x^5)*(1-x)^5) = x^6*(1 + 4*x + 11*x^2 + 25*x^3 + ...).

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A011857 Triangle of numbers [ C(n,k)/k ], k=1..n-1.

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A215052 a(n) = (binomial(n,5) - floor(n/5)) / 5.

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