A051052 -id:A051052 - cp's OEIS frontend

A051036 a(n) = binomial(n, floor(n/4)).

1, 1, 1, 1, 4, 5, 6, 7, 28, 36, 45, 55, 220, 286, 364, 455, 1820, 2380, 3060, 3876, 15504, 20349, 26334, 33649, 134596, 177100, 230230, 296010, 1184040, 1560780, 2035800, 2629575, 10518300, 13884156, 18156204, 23535820, 94143280, 124403620

Offset: 0

N. J. A. Sloane

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A001405, A051033, A051052, A051053, A062947.

a[n_] := Binomial[n, Floor[n/4]]; Array[a, 50, 0] (* Enrique Pérez Herrero, Mar 06 2012 *)

from math import comb
def A051036(n): return comb(n,n>>2) # Chai Wah Wu, Feb 02 2023

A051033 a(n) = binomial(n, floor(n/3)).

Original entry on oeis.org

1, 1, 1, 3, 4, 5, 15, 21, 28, 84, 120, 165, 495, 715, 1001, 3003, 4368, 6188, 18564, 27132, 38760, 116280, 170544, 245157, 735471, 1081575, 1562275, 4686825, 6906900, 10015005, 30045015, 44352165, 64512240, 193536720, 286097760, 417225900, 1251677700

Offset: 0

N. J. A. Sloane

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Cf. A001405, A051036, A051052, A051053, A062947.

Cf. A047193.

Maple
```
[seq(binomial(n,floor(n/3)), n=0..50)];
```

a[n_] := Binomial[n, Floor[n/3]]; Array[a, 50, 0] (* Enrique Pérez Herrero, Mar 06 2012 *)

A051053 a(n) = binomial(n, floor(n/6)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 6, 7, 8, 9, 10, 11, 66, 78, 91, 105, 120, 136, 816, 969, 1140, 1330, 1540, 1771, 10626, 12650, 14950, 17550, 20475, 23751, 142506, 169911, 201376, 237336, 278256, 324632, 1947792, 2324784, 2760681, 3262623, 3838380, 4496388

Offset: 0

N. J. A. Sloane

nonn

Robert Israel, Table of n, a(n) for n = 0..5117

Cf. A001405, A051033, A051036, A051052.

seq(binomial(n, floor(n/6)), n=0..60); # Robert Israel, Mar 11 2018

Table[Binomial[n,Floor[n/6]],{n,0,50}] (* Harvey P. Dale, Dec 18 2013 *)

From Robert Israel, Mar 11 2018: (Start)
Let n = 6*k+j, 0 <= j <= 5.
a(n+6)*(k+1)*Product_{m=1..5} (5*k+j+m) = a(n)*Product_{m=1..6} (6*k+j+m).
a(n) ~ sqrt(3/(5*Pi*k))*(6/5)^j*(6^6/5^5)^k as k -> infinity. (End)

A062947 a(n) = binomial(n,floor(n/7)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 7, 8, 9, 10, 11, 12, 13, 91, 105, 120, 136, 153, 171, 190, 1330, 1540, 1771, 2024, 2300, 2600, 2925, 20475, 23751, 27405, 31465, 35960, 40920, 46376, 324632, 376992, 435897, 501942, 575757, 658008, 749398, 5245786, 6096454, 7059052, 8145060

Offset: 0

Jason Earls, Jul 21 2001

Seiichi Manyama, Table of n, a(n) for n = 0..5000

Cf. A001405, A051036, A051052, A051053.

Table[Binomial[n,Floor[n/7]],{n,50}] (* Harvey P. Dale, Jul 24 2019 *)

j=[]; for(n=1,75,j=concat(j,binomial(n,floor(n/7)))); j

a(0)=1 prepended by Alois P. Heinz, Oct 20 2022

A066704 Triangle with a(n,k) = C(n,floor(n/k)) with n>=k>=1.

Original entry on oeis.org

1, 1, 2, 1, 3, 3, 1, 6, 4, 4, 1, 10, 5, 5, 5, 1, 20, 15, 6, 6, 6, 1, 35, 21, 7, 7, 7, 7, 1, 70, 28, 28, 8, 8, 8, 8, 1, 126, 84, 36, 9, 9, 9, 9, 9, 1, 252, 120, 45, 45, 10, 10, 10, 10, 10, 1, 462, 165, 55, 55, 11, 11, 11, 11, 11, 11, 1, 924, 495, 220, 66, 66, 12, 12, 12, 12, 12, 12

Offset: 1

Henry Bottomley, Jan 14 2002

			Rows start:
  1;
  1,  2;
  1,  3, 3;
  1,  6, 4, 4;
  1, 10, 5, 5, 5;
  ...

Seiichi Manyama, Rows n = 1..140, flattened

Row sums are A051054.
Columns include (most of) A000012, A001405, A051033, A051036, A051052, A051053, A062947 etc.
n appears A008619 times in the n-th row.
Cf. A060539.

A355703 a(n) = binomial(n, floor(log(n))).

Original entry on oeis.org

1, 1, 3, 4, 5, 6, 7, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 1330, 1540, 1771, 2024, 2300, 2600, 2925, 3276, 3654, 4060, 4495, 4960, 5456, 5984, 6545, 7140, 7770, 8436, 9139, 9880, 10660, 11480, 12341, 13244, 14190, 15180, 16215, 17296, 18424, 19600, 20825

Offset: 1

Christoph B. Kassir, Jul 14 2022

nonn

Mathematics Stack Exchange, How to compute asymptotic growth of binomial(n, log(n)).

Cf. A000195, A007318.

Cf. A001405, A051033, A051036, A051052, A051053.

a:= n-> binomial(n, ilog(n)):
seq(a(n), n=1..60);  # Alois P. Heinz, Jul 31 2022

a[n_] := Binomial[n, Floor[Log[n]]]; Array[a, 50] (* Amiram Eldar, Jul 31 2022 *)

a(n) = binomial(n, floor(log(n))); \\ Michel Marcus, Jul 31 2022

from numpy import log
from math import comb, floor
for n in range(1, 50):
    x = comb(n, floor(log(n)))
    print("{}, ".format(x), end='')

cp's OEIS Frontend

A051036 a(n) = binomial(n, floor(n/4)).

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A051033 a(n) = binomial(n, floor(n/3)).

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A051053 a(n) = binomial(n, floor(n/6)).

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Formula

A062947 a(n) = binomial(n,floor(n/7)).

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Extensions

A066704 Triangle with a(n,k) = C(n,floor(n/k)) with n>=k>=1.

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A355703 a(n) = binomial(n, floor(log(n))).

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Author

Keywords

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Programs

Maple

Mathematica

PARI

Python