A171488 Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A005773(n+1)= 1,2,5,13,35,96,267,...

1, 2, 1, 5, 4, 1, 13, 14, 6, 1, 35, 46, 27, 8, 1, 96, 147, 107, 44, 10, 1, 267, 462, 396, 204, 65, 12, 1, 750, 1437, 1404, 858, 345, 90, 14, 1, 2123, 4438, 4835, 3388, 1625, 538, 119, 16, 1, 6046, 13637, 16305, 12802, 7072, 2805, 791, 152, 18, 1

Offset

0,2

Comments

Equal to A064189*B = B*A054336 = B^(-1)*A035324, B = A007318.

Links

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

Formula

Sum_{k, 0<=k<=n} T(n,k)*x^k = A005043(n), A001006(n), A005773(n+1), A059738(n) for x = -2, -1, 0, 1 respectively.

T(n,k) = T(n-1,k-1) + 2*T(n-1,k) + sum_{i, i>=0} T(n-1,k+1+i)*(-1)^i. - Philippe Deléham, Feb 23 2012

T(n,k) = (k+1)*Sum_{j=0..n-k} C(2*j+k,j)*(-1)^j*3^(n-j-k)*C(n+1,j+k+1)/(n+1). - Vladimir Kruchinin Sep 30 2020

Example

Triangle T(n,k) (0<=k<=n) begins:
   1;
   2,   1;
   5,   4,   1;
  13,  14,   6,  1;
  35,  46,  27,  8,  1;
  96, 147, 107, 44, 10, 1;
  ...

Prog

(Maxima)
T(n, k)=((k+1)*sum(binomial(2*j+k, j)*(-1)^j*3^(n-j-k)*binomial(n+1, j+k+1), j, 0, n-k))/(n+1); /* Vladimir Kruchinin Sep 30 2020 */

Crossrefs

Cf. A097609, A064189.

Sequence in context: A318942 A188137 A201165 * A171651 A348451 A104710

Adjacent sequences: A171485 A171486 A171487 * A171489 A171490 A171491

Keyword

nonn,tabl

Author

Philippe Deléham, Dec 10 2009

Status

approved