

A259074


Triangle T(n,k) = Sum_{j=0..(nk)/3} C(n3*j1,k1)*C(nk3*j,j).


0



1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 2, 4, 6, 4, 1, 3, 7, 10, 10, 5, 1, 4, 12, 18, 20, 15, 6, 1, 5, 19, 33, 39, 35, 21, 7, 1, 7, 28, 58, 76, 75, 56, 28, 8, 1, 10, 42, 96, 144, 156, 132, 84, 36, 9, 1, 14, 64, 156, 260, 315, 294, 217, 120, 45, 10, 1, 19, 97, 253, 455, 610, 630, 518, 338, 165, 55, 11, 1
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OFFSET

1,5


LINKS

Table of n, a(n) for n=1..78.


FORMULA

G.f.: (x*y)/(1xx^4x*y).


EXAMPLE

[1]
[1,1]
[1,2,1]
[1,3,3,1]
[2,4,6,4,1]
[3,7,10,10,5,1]


MATHEMATICA

Table[Sum[Binomial[n  3*j  1, k  1] Binomial[n  k  3*j, j], {j, 0, (n  k)/3}], {n, 12}, {k, n}] // Flatten (* Michael De Vlieger, Jun 19 2015 *)


PROG

(Maxima) T(n, k):=sum(binomial(n3*j1, k1)*binomial(nk3*j, j), j, 0, (nk)/3);


CROSSREFS

Column k=1 gives A003269.
Row sums give A008999(n1) for n>0.
Sequence in context: A273108 A306405 A114162 * A162981 A297359 A029264
Adjacent sequences: A259071 A259072 A259073 * A259075 A259076 A259077


KEYWORD

nonn,tabl


AUTHOR

Vladimir Kruchinin, Jun 18 2015


STATUS

approved



