Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7

On the Divisibility of Generalized Central Trinomial Coefficients

Tony D. Noe
14025 NW Harvest Lane
Portland, OR 97229
USA

Abstract: We present several methods of computing sequences of generalized central trinomial coefficients. We generalize the Schur and Holt congruences for Legendre polynomials in order to prove divisibility properties of these sequences and a conjecture of Deutsch and Sagan.

(Concerned with sequences A000984 A001790 A001850 A002426 A006139 A006442 A012000 A026375 A059304 A069835 A080609 A081671 A084601 A084603 A084605 A084609 A084768 A084769 A084770 A084771 A098264 A098265 A098329 A098331 A098332 A098333 A098334 A098335 A098336 A098337 A098338 A098339 A098340 A098341 A098409 A098410 A098430 A098439 A098440 A098441 A098442 A098443 A098444 A098453 A098658 A104454 and A106258 .)

Received December 2 2005; revised version received June 28 2006. Published in Journal of Integer Sequences July 5 2006.