A366978 a(n) = Sum_{j=1..n} binomial(floor(n/j)+n,n+1).

1, 5, 17, 64, 220, 839, 3061, 11684, 44126, 169432, 648589, 2505411, 9670165, 37497431, 145502481, 566076182, 2204451031, 8599761208, 33581164151, 131296796355, 513812162117, 2012709456997, 7890502860027, 30958303856804, 121549519502347, 477555096290870, 1877411492125154

Offset

1,2

Links

Table of n, a(n) for n=1..27.

Formula

a(n) = Sum_{j=1..n} binomial(j+n-1,n)*floor(n/j).

Mathematica

Table[Sum[Binomial[j+n-1, n]Floor[n/j], {j, n}], {n, 30}] (* Harvey P. Dale, Jul 19 2024 *)

Prog

(Python)
from math import isqrt, comb
def A366978(n): return (-(s:=isqrt(n))**2*comb(s+n, n)+sum((q:=n//j)*((n+1)*comb(j+n-1, n)+comb(q+n, n)) for j in range(1, s+1)))//(n+1)

Crossrefs

Superdiagonal of array in A366977.

Sequence in context: A149669 A149670 A149671 * A275220 A062229 A349567

Adjacent sequences: A366975 A366976 A366977 * A366979 A366980 A366981

Keyword

nonn

Author

Chai Wah Wu, Oct 30 2023

Status

approved