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A136216
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Triangle T, read by rows, where T(n,k) = A008544(n-k)*C(n,k) where A008544 equals the triple factorials in column 0.
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4
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1, 2, 1, 10, 4, 1, 80, 30, 6, 1, 880, 320, 60, 8, 1, 12320, 4400, 800, 100, 10, 1, 209440, 73920, 13200, 1600, 150, 12, 1, 4188800, 1466080, 258720, 30800, 2800, 210, 14, 1, 96342400, 33510400, 5864320, 689920, 61600, 4480, 280, 16, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| This array is the particular case P(2,3) of the generalised Pascal triangle P(a,b), a lower unit triangular matrix, shown in the comments to A094587. - Peter Bala (pbala(AT)toucansurf.com), Jul 10 2008
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FORMULA
| Column k of T = column 0 of V^(k+1) for k>=0 where V = A112333. Equals the matrix square of triangle A136215.
T(n,k) = (3*n-3*k-1)*T(n-1,k) + T(n-1,k-1). - Peter Bala (pbala(AT)toucansurf.com), Jul 10 2008
Using the formalism of A132382 modified for the triple rather than the double factorial (replace 2 by 3 in basic formulae), the e.g.f. for the row polynomials is exp(x*t)*(1-3x)^(-2/3). [From Tom Copeland (tcjpn(AT)msn.com), Aug 18 2008]
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EXAMPLE
| Triangle begins:
1;
2, 1;
10, 4, 1;
80, 30, 6, 1;
880, 320, 60, 8, 1;
12320, 4400, 800, 100, 10, 1;
209440, 73920, 13200, 1600, 150, 12, 1;
4188800, 1466080, 258720, 30800, 2800, 210, 14, 1; ...
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PROG
| (PARI) T(n, k)=binomial(n, k)*if(n-k==0, 1, prod(j=0, n-k-1, 3*j+2))
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CROSSREFS
| Cf. A136215 (square-root), A112333, A008544, A136212, A136213.
Cf. A094587.
Sequence in context: A110682 A110327 A105615 * A121334 A126450 A112333
Adjacent sequences: A136213 A136214 A136215 * A136217 A136218 A136219
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Feb 07 2008
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