A064282 Triangle read by rows: T(n,k) = binomial(3n+3, k)*(n-k+1)/(n+1).

1, 1, 3, 1, 6, 12, 1, 9, 33, 55, 1, 12, 63, 182, 273, 1, 15, 102, 408, 1020, 1428, 1, 18, 150, 760, 2565, 5814, 7752, 1, 21, 207, 1265, 5313, 15939, 33649, 43263, 1, 24, 273, 1950, 9750, 35880, 98670, 197340, 246675, 1, 27, 348, 2842, 16443, 71253, 237510

Offset

0,3

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Formula

T(n, k) = T(n-1, k) + 3*T(n-1, k-1) + 3*T(n-1, k-2) + T(n-1, k-3) [starting with T(0,0)=1 and T(n,k)=0 if n < 0 or n < k].

Mathematica

Flatten[Table[Binomial[3n+3, k] (n-k+1)/(n+1), {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Dec 26 2014 *)

Prog

(PARI) { n=-1; for (m=0, 10^9, for (k=0, m, a=binomial(3*m + 3, k)*(m - k + 1)/(m + 1); write("b064282.txt", n++, " ", a); if (n==1000, break)); if (n==1000, break) ) } \\ Harry J. Smith, Sep 11 2009

Crossrefs

Columns include A000012 and A008585. Right hand columns include A001764 and A006630. Row sums are A047099. Triangles A010054 (Triangle Indicator), A007318 (Pascal) and A050166 form a sequence which has this as its next member.

Sequence in context: A084536 A110770 A106855 * A267849 A087644 A049964

Adjacent sequences: A064279 A064280 A064281 * A064283 A064284 A064285

Keyword

nonn,tabl

Author

Henry Bottomley, Sep 24 2001

Status

approved