A239519 a(n) = n + (n-1)*(n-2) + (n-3)*(n-4)*(n-5) + (n-6)*(n-7)*(n-8)*(n-9) + ... + ...*1.

0, 1, 3, 5, 11, 19, 32, 62, 112, 191, 316, 558, 988, 1711, 2864, 4661, 7703, 12883, 21626, 35989, 58826, 94217, 150017, 239047, 382676, 614425, 984452, 1565021, 2458810, 3826746, 5918938, 9136603, 14115710, 21842345, 33804340, 52186061, 80128082, 122221802

Offset

0,3

Comments

In other words, write n,n-1,n-2,...,n-k,...,1 and place '+' before the terms n-k, where k is triangular, place '*' elsewhere, then a(n) = result. - Ralf Stephan, Mar 29 2014

Links

Table of n, a(n) for n=0..37.

Example

a(2) = 2 + 1 = 3.
a(3) = 3 + 2*1 = 5.
a(9) = 9 + 8*7 + 6*5*4 + 3*2*1 = 191.
a(10) = 10 + 9*8 + 7*6*5 + 4*3*2*1 = 316.

Prog

(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)+', ',

Crossrefs

Cf. A227363-A227367.

Sequence in context: A127453 A092602 A134127 * A329178 A298348 A303005

Adjacent sequences: A239516 A239517 A239518 * A239520 A239521 A239522

Keyword

nonn

Author

Alex Ratushnyak, Mar 20 2014

Status

approved