A068241 1/2 the number of colorings of a 5 X 5 square array with n colors.

1, 290493, 10221446382, 25410195205090, 10988934663584655, 1515888422040128871, 94793386050673781548, 3330373652089796835972, 75543449548467802433805, 1216257376373886871239985, 14865437328242111405302266, 144907139188443182894343078

Offset

2,2

Links

Alois P. Heinz, Table of n, a(n) for n = 2..1000

Formula

From Alois P. Heinz, Apr 27 2012 (Start)

G.f.: (64045717133*x^23 +99613598986379*x^22 +30122616672179057*x^21 +2905816841816465011*x^20 +116885162434957285435*x^19 +2301461202426082443493*x^18 +24565180390104215669199*x^17 +152051416127748639010437*x^16 +570955972331169762888066*x^15 +1339611184016759341097870*x^14 +1999028208566595454861898*x^13 +1912423825883782158177854*x^12 +1171838449935804166262422*x^11 +455354414964383806296586*x^10 +109981844564513940260830*x^9 +15982890606970244203818*x^8 +1330217331928452928929*x^7 +58885777127277221367*x^6 +1238407862810793461*x^5 +10331590803059615*x^4 +25144532006783*x^3 +10213893889*x^2 +290467*x+1)*x^2 / (x-1)^26.

a(n) = n*(n-1)*(n^23 -39*n^22 +741*n^21 -9123*n^20 +81675*n^19 -565677*n^18 +3148503*n^17 -14442408*n^16 +55554975*n^15 -181400963*n^14 +507043269*n^13 -1219915634*n^12 +2534102852*n^11 -4548768800*n^10 +7046057296*n^9 -9383152441*n^8 +10671809555*n^7 -10260465459*n^6 +8212654097*n^5 -5348136944*n^4 +2734090327*n^3 -1033880579*n^2 +258309564*n -32126211)/2.

(End)

Maple

a:= n-> n*(n-1)*(-32126211 +(258309564 +(-1033880579 +(2734090327 +(-5348136944 +(8212654097 +(-10260465459 +(10671809555 +(-9383152441 +(7046057296 +(-4548768800 +(2534102852 +(-1219915634 +(507043269 +(-181400963 +(55554975 +(-14442408 +(3148503 +(-565677 +(81675 +(-9123+(741 +(-39+n)*n) *n)*n)*n)*n) *n)*n)*n) *n)*n)*n) *n)*n)*n) *n)*n)*n) *n)*n)*n) *n)*n)/2:
seq(a(n), n=2..30); # Alois P. Heinz, Apr 27 2012

Crossrefs

Cf. A068239-A068305, A000332, A002417, A027441, A182368, A182406.

Sequence in context: A237556 A121742 A093792 * A250618 A252992 A253532

Adjacent sequences: A068238 A068239 A068240 * A068242 A068243 A068244

Keyword

nonn

Author

R. H. Hardin, Feb 24 2002

Status

approved