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A159841 Triangle T(n,k) = binomial(3*n+1, 2*n+k+1), read by rows. 4
1, 4, 1, 21, 7, 1, 120, 45, 10, 1, 715, 286, 78, 13, 1, 4368, 1820, 560, 120, 16, 1, 27132, 11628, 3876, 969, 171, 19, 1, 170544, 74613, 26334, 7315, 1540, 231, 22, 1, 1081575, 480700, 177100, 53130, 12650, 2300, 300, 25, 1, 6906900, 3108105, 1184040, 376740 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

T(n,0) = A045721(n), T(2n,n) = A079590(n).

LINKS

G. C. Greubel, Rows n=0..100 of triangle, flattened

E. H. M. Brietzke, An identity of Andrews and a new method for the Riordan array proof of combinatorial identities, Discrete Math., 308 (2008), 4246-4262.

FORMULA

T(n,0) = 4*T(n-1,0) + 5*T(n-1,1) + T(n-1,2), T(n+1,k+1) = T(n,k) + 3*T(n,k+1) + 3*T(n,k+2) + T(n,k+3) for k >= 0.

EXAMPLE

Triangle begins:

     1;

     4,    1;

    21,    7,    1;

   120,   45,   10,    1;

   715,  286,   78,   13,    1;

  4368, 1820,  560,  120,   16,    1;

  ...

MATHEMATICA

f[n_, k_]:=Binomial[3n+1, 2n+k+1]; Table[ f[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Robert G. Wilson v, May 31 2009 *)

PROG

(PARI) for(n=0, 10, for(k=0, n, print1(binomial(3*n+1, 2*n+k+1), ", "))) \\ G. C. Greubel, May 19 2018

(MAGMA) /* As triangle */ [[Binomial(3*n+1, 2*n+k+1): k in [0..n]]: n in [0..10]]; // G. C. Greubel, May 19 2018

CROSSREFS

Cf. A045721, A079590.

Sequence in context: A144484 A121336 A126457 * A202550 A142472 A299445

Adjacent sequences:  A159838 A159839 A159840 * A159842 A159843 A159844

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Apr 23 2009

EXTENSIONS

More terms from Robert G. Wilson v, May 31 2009

STATUS

approved

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Last modified August 9 01:35 EDT 2020. Contains 336310 sequences. (Running on oeis4.)