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A211230 Matrix square of lower triangular array A211226. 2
1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 8, 8, 6, 4, 1, 8, 8, 8, 6, 2, 1, 20, 24, 24, 24, 9, 6, 1, 16, 20, 24, 24, 12, 9, 2, 1, 48, 64, 80, 96, 48, 48, 12, 8, 1, 32, 48, 64, 80, 48, 48, 16, 12, 2, 1, 112, 160, 240, 320, 200, 240, 80, 80, 15, 10, 1, 64, 112, 160, 240, 160 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Analog of square of Pascal's triangle.

LINKS

Table of n, a(n) for n=0..70.

FORMULA

T(2*n,2*k) = T(2*n+1,2*k+1) = (n+2-k)*binomial(n,k)*2^(n-k-1);

T(2*n,2*k+1) = n*binomial(n-1,k)*2^(n-k); T(2*n+1,2*k) = binomial(n,k)*2^(n-k+1).

Recurrence equations:

T(2*n,2*k) = n/k*T(2*n-1,2*k-1), T(2*n,2*k+1) = n*T(2*n-1,2*k);

T(2*n+1,2*k) = 1/k*T(2*n,2*k-1), T(2*n+1,2*k+1) = T(2*n,2*k).

O.g.f.: P(x,t)/Q(x,t), where P(x,t) = 1 + (x+2)*t - (1-x)^2*t^2 - (x^3+2*x^2+x+4)*t^3 and Q(x,t) = (1-(x^2+2)*t^2)^2.

Row polynomials:

R(2*n,x) = (x^2+2*n*x+n+2)*(x^2+2)^(n-1);

R(2*n+1,x) = (x^3+2*x^2+(n+2)*x+4)*(x^2+2)^(n-1).

Column 0 = A211227. Row sums A211231.

EXAMPLE

Triangle begins

.n\k.|....0....1....2....3....4....5....6....7....8....9

= = = = = = = = = = = = = = = = = = = = = = = = = = = = =

..0..|....1

..1..|....2....1

..2..|....3....2....1

..3..|....4....3....2....1

..4..|....8....8....6....4....1

..5..|....8....8....8....6....2....1

..6..|...20...24...24...24....9....6....1

..7..|...16...20...24...24...12....9....2....1

..8..|...48...64...80...96...48...48...12....8....1

..9..|...32...48...64...80...48...48...16...12....2....1

...

CROSSREFS

Cf. A211226, A211231 (row sums).

Sequence in context: A052310 A052313 A271355 * A049085 A193173 A227355

Adjacent sequences:  A211227 A211228 A211229 * A211231 A211232 A211233

KEYWORD

nonn,easy,tabl

AUTHOR

Peter Bala, Apr 05 2012

STATUS

approved

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Last modified December 6 06:58 EST 2016. Contains 278775 sequences.