A087422 Number of terms in the expansion of Product(x_i + x_{i+1} + ... + x_j) over 1 <= i < j <= n.

1, 1, 2, 8, 55, 567, 7958, 142396, 3104160, 79813513

Offset

0,3

Comments

The sum of the coefficients in the expansion of this product are the superfactorials A000178. - Robert G. Wilson v, Aug 02 2005

Links

Table of n, a(n) for n=0..9.

Example

a(3) = 8 because the expansion of (x+y)(y+z)(x+y+z) = x^2y + x^2z + 2xy^2 + 3xyz + xz^2 + y^3 + 2y^2z + yz^2 has 8 terms.

Maple

a:= n-> nops(expand(mul(mul(add(x[k], k=i..j), i=1..j-1), j=2..n))):
seq(a(n), n=0..8);  # Alois P. Heinz, Jul 07 2023

Mathematica

f[1]=1; f[n_] := Block[{lst = Take[{a, b, c, d, e, f, g, h, i}, n], s = 1}, Do[s = s*Times @@ Plus @@@ Partition[lst, i, 1], {i, 2, n}]; Length@Expand@s]; Do[ Print@ f@n, {n, 9}] (* Robert G. Wilson v, Sep 18 2006 *)

Crossrefs

Cf. A000178.

Sequence in context: A377098 A380020 A134954 * A081667 A117496 A117564

Adjacent sequences: A087419 A087420 A087421 * A087423 A087424 A087425

Keyword

nonn,more

Author

Alex Postnikov (apost(AT)math.mit.edu), Oct 22 2003

Extensions

a(8) from Robert G. Wilson v, Apr 26 2005

a(9) from Vaclav Kotesovec, Apr 09 2021

a(0)=1 prepended by Alois P. Heinz, Jul 07 2023

Status

approved