%I #7 Jun 18 2022 19:20:10

%S 4,208,38112,8002304,858105364,48452117136,1706069013928,

%T 41801237632858,764295988745248,10946853015640490,127331263486979692,

%U 1237140566105421398,10270879068733905810,74243436332274681890

%N Number of n X 5 0..3 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.

%C Column 5 of A201981.

%H R. H. Hardin, <a href="/A201978/b201978.txt">Table of n, a(n) for n = 1..126</a>

%F Empirical: a(n) = (2978188707224921/132626429906095529318154240000000)*n^30 + (26309065116080869/8841761993739701954543616000000)*n^29 + (145497589435437061/914665033835141581504512000000)*n^28 + (3537283836553603/967899506703853525401600000)*n^27 + (1741689049637834987/72592463002789014405120000000)*n^26 - (1167647663123681/2312230068571078656000000)*n^25 + (23056825693957945811/4690589917103290161561600000)*n^24 - (5789170705185949/735778810526006299852800)*n^23 + (4689758223655379298751/1019693460239845687296000000)*n^22 - (562745332264128997/3233888207791718400000)*n^21 + (44013155552080990347511/9711366287998530355200000)*n^20 - (585393739213952456071/5440541337814302720000)*n^19 + (1662987485676029915481620389/697684999111473364992000000)*n^18 - (438246685927013505733133351/9302466654819644866560000)*n^17 + (6682832018365291737859985849/8208058813076157235200000)*n^16 - (319338881192306947330636787/26057329565321134080000)*n^15 + (1331350912029007045659306549953/8305773798946111488000000)*n^14 - (2759081354085794867683805791/1521203992480972800000)*n^13 + (21091962385847268741889025789117/1194953273718569164800000)*n^12 - (17004169591405004217594327807229/115874256845437009920000)*n^11 + (3862680018589482050378751273259289/3734228980370528640000000)*n^10 - (29799003492477365417301080765021/4863464687499264000000)*n^9 + (43872824564050051319425191543596017/1454175941562279936000000)*n^8 - (33087574139635229188975549150501/271554797677363200000)*n^7 + (7291187366314988698913065464679554007/18379168150301038080000000)*n^6 - (103944019954125679560797511222064289/102106489723894656000000)*n^5 + (6114531409859879267523302791762699/3063194691716839680000)*n^4 - (987983953622737130846968099/345425816736000)*n^3 + (16275537053027023619213913467/5828546630907000)*n^2 - (28905264430368909791279/17644617900)*n + 428055727992.

%e Some solutions for n=3

%e ..0..1..2..3..3....0..0..1..1..3....0..2..3..3..3....0..0..1..2..2

%e ..3..2..2..1..1....0..2..3..3..2....0..3..2..2..2....2..2..1..0..1

%e ..3..3..1..1..1....2..1..0..0..0....2..0..0..0..0....3..3..2..2..0

%Y Cf. A201981.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 07 2011