A227363 a(n) = n + (n-1)*(n-2) + (n-3)*(n-4)*(n-5) + (n-6)*(n-7)*(n-8)*(n-9) + ... + ...*(n-n).

0, 1, 2, 5, 10, 17, 32, 61, 110, 185, 316, 557, 986, 1705, 2840, 4661, 7702, 12881, 21620, 35965, 58706, 94217, 150016, 239045, 382670, 614401, 984332, 1564301, 2458810, 3826745, 5918936, 9136597, 14115686, 21842225, 33803620, 52181021, 80128082, 122221801, 185211440

Offset: 0

Author

Alex Ratushnyak, Jul 07 2013

Keywords

• nonn

Comments

From a question by Jonathan Vos Post dated Jul 09 2013, the indices of a(n) which are prime begin: 2, 3, 5, 7, 11, 41, 111, 205, 211, 215, 341, 345, 395, 581, 585, 1221, ..., . - Robert G. Wilson v, Jul 10 2013

Examples

			a(2) = 2 + 1*0 = 2.
a(3) = 3 + 2*1 = 5.
a(9) = 9 + 8*7 + 6*5*4 + 3*2*1*0 = 9 + 56 + 120 = 185.
a(11) = 11 + 10*9 + 8*7*6 + 5*4*3*2 = 557.
a(18) = 18 + 17*16 + 15*14*13 + 12*11*10*9 + 8*7*6*5*4 = 21620.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A227364, A227365, A227366, A227367.

Programs

Mathematica

f[n_] := Sum[ Product[ n - k (k - 1)/2 - i + 1, {i, k}], {k, Sqrt[ 2n]}]; Array[f, 39, 0] (* Robert G. Wilson v, Jul 10 2013 *)

PARI

a(n)=sum(k=1,sqrtint(2*n)+1,prod(i=1,k,max(n-k*(k-1)/2-i+1,0))) \\ Charles R Greathouse IV, Jul 09 2013

Python

for n in range(55):
  sum = i = 0
  k = 1
  while i<=n:
    product = 1
    for x in range(k):
      product *= n-i
      i += 1
      if i>n: break
    sum += product
    k += 1
  print(str(sum), end=',')