Multinomial Series

Author

Eric W. Weisstein
January 16, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Combinatorics/MultinomialSeries.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/MultinomialSeries.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Examples

Expand[((((Subscript[a, 1])+(Subscript[a, 2])+(Subscript[a, 3])))^3)]

Sum[(((n1+n2+n3)!)/(n1!n2!n3!))((Subscript[a, 1])^n1)((Subscript[a, 2])^n2)((Subscript[a, 3])^n3)/.n3->3-n1-n2,{n1,0,3},{n2,0,3-n1}]

Expand[((((Subscript[a, 1])+(Subscript[a, 2])+(Subscript[a, 3])))^4)]

Sum[(((n1+n2+n3)!)/(n1!n2!n3!))((Subscript[a, 1])^n1)((Subscript[a, 2])^n2)((Subscript[a, 3])^n3)/.n3->4-n1-n2,{n1,0,4},{n2,0,4-n1}]