A167751 -id:A167751 - cp's OEIS frontend

A167753 Hankel transform of A167751.

1, 1, 0, -1, -1, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1

Offset: 0

Paul Barry, Nov 10 2009

sign

The nonzero terms appear to be indexed by ceiling((n+1)^2/4) - 0^n (see A004652).

Cf. A167752.

A167749 Riordan array (1,xf(x)) where f(x) is the g.f. of A005169 (fountains of coins).

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 2, 3, 3, 1, 0, 3, 6, 6, 4, 1, 0, 5, 11, 13, 10, 5, 1, 0, 9, 20, 27, 24, 15, 6, 1, 0, 15, 38, 54, 55, 40, 21, 7, 1, 0, 26, 70, 109, 120, 100, 62, 28, 8, 1, 0, 45, 129, 216, 258, 236, 168, 91, 36, 9, 1, 0, 78, 238, 423, 544, 540, 426, 266, 128, 45, 10, 1

Offset: 0

Paul Barry, Nov 10 2009

Row sums are A167750. Diagonal sums are A167751.

			Triangle begins
1,
0, 1,
0, 1, 1,
0, 1, 2, 1,
0, 2, 3, 3, 1,
0, 3, 6, 6, 4, 1,
0, 5, 11, 13, 10, 5, 1,
0, 9, 20, 27, 24, 15, 6, 1,
0, 15, 38, 54, 55, 40, 21, 7, 1,
0, 26, 70, 109, 120, 100, 62, 28, 8, 1,
0, 45, 129, 216, 258, 236, 168, 91, 36, 9, 1,
0, 78, 238, 423, 544, 540, 426, 266, 128, 45, 10, 1,
0, 135, 437, 824, 1127, 1205, 1035, 721, 402, 174, 55, 11, 1

G.f.: 1/(1-xy/(1-x/(1-x^2/(1-x^3/(1-x^4/(1-... (continued fraction).

cp's OEIS Frontend

A167753 Hankel transform of A167751.

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A167749 Riordan array (1,xf(x)) where f(x) is the g.f. of A005169 (fountains of coins).

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