A241205 Sum of x*y^2*z^3 for positive integers x,y,z with x + y + z = n.

0, 0, 1, 14, 95, 436, 1554, 4632, 12078, 28380, 61347, 123838, 236093, 428792, 746980, 1255008, 2042652, 3232584, 4989381, 7530270, 11137819, 16174796, 23101430, 32495320, 45074250, 61722180, 83518695, 111772206, 148057209, 194255920, 252604616, 325745024, 416781112, 529341648, 667648905

Offset

1,4

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = n^2*(n-1)*(n-2)*(n+2)*(n+1)*(3*n^2+1)/10080. - corrected by Eric Rowland, Aug 15 2017

G.f: x^3*(1+x)*(1+4*x+x^2)/(1-x)^9.

Example

For n=3 the only positive integer solution to x+y+z=3 is (1,1,1) so a(3) = 1.
For n=4 the solutions are (1,1,2),(1,2,1),(2,1,1) so a(4) = 2^3 + 2^2 + 2 = 14.

Maple

A241205:= n -> n^2*(n-1)*(n-2)*(n+2)*(n+1)*(3*n^2+1)/10080; # Robert Israel, Apr 17 2014

Mathematica

Rest[CoefficientList[Series[x^3 (1 + x) (1 + 4 x + x^2)/(1 - x)^9, {x, 0, 35}], x]] (* Vincenzo Librandi, Jul 01 2014 *)

Crossrefs

Sequence in context: A101383 A044265 A044646 * A055844 A308821 A274724

Adjacent sequences: A241202 A241203 A241204 * A241206 A241207 A241208

Keyword

nonn,easy

Author

Robert Israel, Apr 17 2014

Status

approved