38107 組合恆等式 $\sum_k\binom{2k}{k}\binom{2(n-k)}{n-k} = 4^n$ 的兩個證明

★ 終極密碼為0到100之間 ★

一、前言

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參考資料

Valerio De Angelis, Pairings and signed permutations, Amer. Math. Monthly 113 (2006), no. 7, 642--644. MR2252934 Richard P. Stanley, Enumerative combinatorics. {Vol. 1}, Cambridge Studies in Advanced Mathematics, vol. 49, Cambridge University Press, Cambridge, 1997, With a foreword by Gian-Carlo Rota, Corrected reprint of the 1986 original. MR1442260 (98a:05001) Richard P. Stanley, Enumerative combinatorics. {Vol. 2}, Cambridge Studies in Advanced Mathematics, vol. 62, Cambridge University Press, Cambridge, 1999, With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin. MR1676282 (2000k: 05026) Marta Sved, Counting and recounting, Math. Intelligencer 5 (1983), no. 4, 21--26. MR746893 (85g:05013) Marta Sved, Counting and recounting: the aftermath, Math. Intelligencer 6 (1984), no. 4, 44--45. MR762059 (86f:05016)

---本文作者任教國立台灣師範大學數學系---