A127501 Triangle read by rows :T(n,k)=Sum_{j, j>=0}A089942(n,j)*binomial(j,k).

1, 1, 1, 3, 3, 1, 7, 10, 5, 1, 19, 31, 21, 7, 1, 51, 96, 79, 36, 9, 1, 141, 294, 282, 159, 55, 11, 1, 393, 897, 972, 645, 279, 78, 13, 1, 1107, 2727, 3273, 2475, 1269, 447, 105, 15, 1, 3139, 8272, 10835, 9136, 5369, 2254, 671, 136, 17, 1

Offset

0,4

Comments

Riordan array (1/sqrt(1-2*x-3*x^2), (1+x-sqrt(1-2*x-3*x^2))/(2*sqrt(1-2*x-3*x^2)). - Philippe Deléham, Mar 06 2013

Links

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

Formula

T(n+1,1)=A055217(n) . Sum_{k, 0<=k<=n}T(n,k)*x^k = A033999(n), A005043(n), A002426(n), A112657(n) for x = -2, -1, 0, 1 respectively.

Example

Triangle begins:
1;
1, 1;
3, 3, 1;
7, 10, 5, 1;
19, 31, 21, 7, 1;
51, 96, 79, 36, 9, 1;
141, 294, 282, 159, 55, 11, 1;
393, 897, 972, 645, 279, 78, 13, 1;
1107, 2727, 3273, 2475, 1269, 447, 105, 15, 1;
3139, 8272, 10835, 9136, 5369, 2254, 671, 136, 17, 1; ...

Crossrefs

Sequence in context: A116401 A106479 A114422 * A181304 A339435 A118408

Adjacent sequences: A127498 A127499 A127500 * A127502 A127503 A127504

Keyword

nonn,tabl

Author

Philippe Deléham, Apr 01 2007

Status

approved