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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 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.