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 A107676 Matrix cube of triangle A107671. 6
 1, 56, 8, 7965, 513, 27, 2128064, 81856, 2368, 64, 914929500, 23846125, 469625, 7625, 125, 576689214816, 10943504136, 160767720, 1898856, 19656, 216, 500750172337212, 7250862593527, 83548607478, 776598305, 6081733, 43561, 343 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Column 0 is A006690. LINKS FORMULA Matrix diagonalization method: define triangular matrix P by P(n, k) = ((n+1)^3)^(n-k)/(n-k)!, n>=k>=0 and diagonal matrix D(n, n) = n+1, then T is given by T = P^-1*D^3*P. EXAMPLE Triangle begins: 1; 56,8; 7965,513,27; 2128064,81856,2368,64; 914929500,23846125,469625,7625,125; 576689214816,10943504136,160767720,1898856,19656,216; ... which equals the matrix cube of triangle A107671: 1; 8,2; 513,27,3; 81856,2368,64,4; 23846125,469625,7625,125,5; 10943504136,160767720,1898856,19656,216,6; ... PROG (PARI) {T(n, k)=local(P=matrix(n+1, n+1, r, c, if(r>=c, (r^3)^(r-c)/(r-c)!)), D=matrix(n+1, n+1, r, c, if(r==c, r))); if(n>=k, (P^-1*D^3*P)[n+1, k+1])} CROSSREFS Cf. A107667, A107671, A107674, A006690. Sequence in context: A206786 A036197 A182355 * A005932 A109737 A092077 Adjacent sequences:  A107673 A107674 A107675 * A107677 A107678 A107679 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Jun 07 2005 STATUS approved

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Last modified December 4 02:40 EST 2021. Contains 349469 sequences. (Running on oeis4.)