A054336 -id:A054336 - cp's OEIS frontend

A171509 Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A126931.

1, 3, 1, 10, 6, 1, 33, 29, 9, 1, 110, 126, 57, 12, 1, 366, 518, 306, 94, 15, 1, 1220, 2052, 1494, 600, 140, 18, 1, 4065, 7925, 6849, 3389, 1035, 195, 21, 1, 13550, 30030, 30025, 17628, 6635, 1638, 259, 24, 1

Offset: 0

Philippe Deléham, Dec 10 2009

Equal to A053121*B^3, B = A007318.

			Triangle begins:
  1 ;
  3,1 ;
  10,6,1 ;
  33,29,9,1 ;
  110,126,57,12,1 ; ...

Cf. A053121, A054336, A096164, A171505.

Sum_{k=0..n} T(n,k)*x^k = A126930(n), A126120(n), A001405(n), A054341(n), A126931(n) for x = -4, -3, -2, -1, 0 respectively.

T(n,k) = T(n-1,k-1) + 3*T(n-1,k) + Sum_{i>=0} T(n-1,k+1+i)*(-3)^i. - Philippe Deléham, Feb 23 2012

A202847 Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A126930.

Original entry on oeis.org

1, -1, 1, 2, -2, 1, -3, 5, -3, 1, 6, -10, 9, -4, 1, -10, 22, -22, 14, -5, 1, 20, -44, 54, -40, 20, -6, 1, -35, 93, -123, 109, -65, 27, -7, 1, 70, -186, 281, -276, 195, -98, 35, -8, 1, -126, 386, -618, 682, -541, 321, -140, 44, -9, 1

Offset: 0

Philippe Deléham, Mar 02 2013

			Triangle begins
1
-1, 1
2, -2, 1
-3, 5, -3, 1
6, -10, 9, -4, 1
-10, 22, -22, 14, -5, 1
20, -44, 54, -40, 20, -6, 1
-35, 93, -123, 109, -65, 27, -7, 1
...
Production matrix begins
x, 1
1, x, 1
1, 1, x, 1
1, 1, 1, x, 1
1, 1, 1, 1, x, 1
1, 1, 1, 1, 1, x, 1
1, 1, 1, 1, 1, 1, x, 1
1, 1, 1, 1, 1, 1, 1, x, 1
1, 1, 1, 1, 1, 1, 1, 1, x, 1
1, 1, 1, 1, 1, 1, 1, 1, 1, x, 1
..., with x = -1.

Cf. (sequences with similar production matrix) A097609 (x=0), A033184 (x=1), A104259 (x=2), A171568 (x=3), A171589 (x=4)

T(n,k) = (-1)^(n-k)*A054336(n,k).

Sum_{k, 0<=k<=n}T(n,k)*x^k = (-1)^n*A126931(n), (-1)^n*A054341(n), A126930(n), A126120(n), A001405(n), A054341(n), A126931(n) for x = -2, -1, 0, 1, 2, 3, 4 respectively.

cp's OEIS Frontend

A171509 Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A126931.

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