A187552 Triangle a(n,k) = binomial(n,k)*binomial(n+1,k+1)*binomial(n+2,k+2) read by rows.

1, 6, 1, 18, 24, 1, 40, 180, 60, 1, 75, 800, 900, 120, 1, 126, 2625, 7000, 3150, 210, 1, 196, 7056, 36750, 39200, 8820, 336, 1, 288, 16464, 148176, 308700, 164640, 21168, 504, 1, 405, 34560, 493920, 1778112, 1852200, 564480, 45360, 720, 1, 550, 66825, 1425600, 8149680, 14669424, 8731800, 1663200, 89100, 990, 1, 726, 121000, 3675375, 31363200, 89646480, 92207808, 34303500, 4356000, 163350, 1320, 1

Offset

0,2

Comments

Row sums are 1, 7, 43, 281, 1896, 13112, 92359,...

Links

Table of n, a(n) for n=0..65.

Example

Triangle begins:
1
6,1
18,24,1
40,180,60,1
75,800,900,120,1
126,2625,7000,3150,210,1
196,7056,36750,39200,8820,336,1
288,16464,148176,308700,164640,21168,504,1
405,34560,493920,1778112,1852200,564480,45360,720,1

Maple

A187552 := proc(n, k) binomial(n, k)*binomial(n+1, k+1)*binomial(n+2, k+2) ; end proc:

Mathematica

Table[Binomial[n, k]Binomial[n + 1, k + 1]Binomial[n + 2, k + 2], {n, 0, 8}, {k, 0, 8}]//MatrixForm

Prog

(Maxima) create_list(binomial(n, k)*binomial(n+1, k+1)*binomial(n+2, k+2), n, 0, 8, k, 0, n);

Crossrefs

Cf. A103371, A002411 (column k=0), A165187 (column k=1), A007531 (subdiagonal)

Sequence in context: A369904 A373573 A092371 * A157386 A157396 A019430

Adjacent sequences: A187549 A187550 A187551 * A187553 A187554 A187555

Keyword

nonn,easy,tabl

Author

Emanuele Munarini, Mar 11 2011

Status

approved