A298309 Triangle read by rows: T(n,m) = Sum_{i=0..n+1} C(n-i+1,i-1)*C(n-i+1,i)*C(n-i+1,m-i+1).

0, 1, 1, 2, 4, 2, 3, 11, 13, 5, 4, 25, 51, 43, 13, 5, 49, 149, 203, 130, 32, 6, 86, 364, 716, 734, 382, 80, 7, 139, 787, 2099, 3061, 2521, 1105, 201, 8, 211, 1553, 5385, 10455, 12093, 8311, 3143, 505, 9, 305, 2851, 12473, 30918, 47064, 45075, 26581, 8843, 1273

Offset

0,4

Links

Table of n, a(n) for n=0..54.

Formula

G.f.: ((1-(1-x*y)*(x*y+x))/sqrt((1-(x*y+1)*(x*y+x))^2-4*x*y*(x*y+x)^2)-1)/(2*x*y).

Example

Triangle begins
  0;
  1,    1;
  2,    4,    2;
  3,   11,   13,    5;
  4,   25,   51,   43,   13;
  5,   49,  149,  203,  130,   32;
  6,   86,  364,  716,  734,  382,   80;
  7,  139,  787, 2099, 3061, 2521, 1105,  201;

Prog

(Maxima)
T(n, m):=sum(binomial(n-i+1, i-1)*binomial(n-i+1, i)*binomial(n-i+1, m-i+1), i, 0, n+1);
(PARI) T(n, m) = sum(i=0, n+1, binomial(n-i+1, i-1)*binomial(n-i+1, i)*binomial(n-i+1, m-i+1));
tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print()); \\ Michel Marcus, Jan 19 2018

Crossrefs

T(n,n) is A110320(n).

Sequence in context: A368434 A134400 A016095 * A349205 A181399 A349207

Adjacent sequences: A298306 A298307 A298308 * A298310 A298311 A298312

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Jan 17 2018

Status

approved