Journal of Integer Sequences, Vol. 15 (2012), Article 12.1.8

Families of Sequences From a Class of Multinomial Sums

Martin Griffiths
Department of Mathematical Sciences
University of Essex
United Kingdom


In this paper we obtain formulas for certain sums of products involving multinomial coefficients and Fibonacci numbers. The sums studied here may be regarded as generalizations of the binomial transform of the sequence comprising the even-numbered terms of the Fibonacci sequence. The general formulas, involving both Fibonacci and Lucas numbers, give rise to infinite sequences that are parameterized by two positive integers. Links to the exponential partial Bell polynomials are also established.

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(Concerned with sequences A087426 A093131)

Received October 6 2011; revised version received December 27 2011. Published in Journal of Integer Sequences, December 27 2011.

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