A238241 Riordan array (1/(1-x-x^2)^2, x/(1-x-x^2)^2).

1, 2, 1, 5, 4, 1, 10, 14, 6, 1, 20, 40, 27, 8, 1, 38, 105, 98, 44, 10, 1, 71, 256, 315, 192, 65, 12, 1, 130, 594, 924, 726, 330, 90, 14, 1, 235, 1324, 2534, 2472, 1430, 520, 119, 16, 1, 420, 2860, 6588, 7776, 5522, 2535, 770, 152, 18, 1, 744, 6020, 16407, 22968

Offset

0,2

Comments

Row sums are A097472(n).

Links

Table of n, a(n) for n=0..58.

Formula

T(n,k) = A037027(n+k+1, 2*k+1).

T(n,k) = T(n-1,k-1) + 2*T(n-1,k) + T(n-2,k) - 2*T(n-3,k) - T(n-4,k), T(0,0) = 1, T(n,k) = 0 if k<0 or if k>n.

G.f.: -1/(x*y-x^4-2*x^3+x^2+2*x-1). - Vladimir Kruchinin, Apr 29 2015

Example

Triangle begins:
1;
2, 1;
5, 4, 1;
10, 14, 6, 1;
20, 40, 27, 8, 1;
38, 105, 98, 44, 10, 1;
71, 256, 315, 192, 65, 12, 1;
130, 594, 924, 726, 330, 90, 14, 1;
...

Mathematica

T[0, 0] = 1; T[n_, k_] := SeriesCoefficient[-1/(x*y - x^4 - 2*x^3 + x^2 + 2*x - 1), {x, 0, n}, {y, 0, k}]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 29 2015, after Vladimir Kruchinin *)

Crossrefs

Cf. A037027, A152440

Cf. Diagonals: A000012, A005843, A014106

Cf. Columns: A001629, A001872, A001874

Sequence in context: A157011 A246173 A092821 * A299444 A371300 A110552

Adjacent sequences: A238238 A238239 A238240 * A238242 A238243 A238244

Keyword

nonn,tabl

Author

Philippe Deléham, Feb 20 2014

Status

approved