A257558 Triangle, read by rows, T(n,k) = k*Sum_{i=0..(n-k)/2} C(k,i)*C(2*n-k-4*i-1,n-2*i-k)/(n-2*i).

1, 1, 1, 3, 2, 1, 6, 7, 3, 1, 16, 18, 12, 4, 1, 47, 53, 37, 18, 5, 1, 146, 162, 120, 64, 25, 6, 1, 471, 518, 390, 227, 100, 33, 7, 1, 1562, 1708, 1299, 788, 385, 146, 42, 8, 1, 5291, 5762, 4410, 2750, 1426, 606, 203, 52, 9, 1, 18226, 19788, 15216, 9664, 5225, 2388, 903, 272, 63, 10, 1

Offset

1,4

Links

Indranil Ghosh, Rows 1..100, flattened

Formula

G.f.: 1/(1-C(x)*(x+x^3)*y)-1, where C(x) is g.f. of Catalan numbers (A000108).

Example

1;
1, 1;
3, 2, 1;
6, 7, 3, 1;
16, 18, 12, 4, 1;
47, 53, 37, 18, 5, 1;

Mathematica

Flatten[Table[k*Sum[Binomial[k, i] * Binomial[2n-k-4i-1, n-2i-k] / (n-2i), {i, 0, (n-k)/2}], {n, 1, 11}, {k, 1, n}]] (* Indranil Ghosh, Mar 04 2017 *)

Prog

(Maxima)
T(n, k):=(k*sum((binomial(k, i)*binomial(2*n-k-4*i-1, n-2*i-k))/(n-2*i), i, 0, (n-k)/2));
(PARI)
tabl(nn) = {for (n=1, nn, for(k=1, n, print1(k*sum(i=0, (n-k)/2, binomial(k, i) * binomial(2*n-k-4*i-1, n-2*i-k) / (n-2*i)), ", "); ); print(); ); };
tabl(11); \\ Indranil Ghosh, Mar 04 2017

Crossrefs

Cf. A000108.

Sequence in context: A208518 A139624 A132276 * A202390 A210858 A114586

Adjacent sequences: A257555 A257556 A257557 * A257559 A257560 A257561

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Apr 30 2015

Status

approved