A188463 Coefficient array of the second column of the inverse of the Riordan array ((1+(r+1)x)/(1+(r+2)x+rx^2), x/(1+(r+2)x+rx^2)).

1, 3, 1, 7, 7, 1, 15, 30, 12, 1, 31, 103, 79, 18, 1, 63, 312, 387, 166, 25, 1, 127, 873, 1586, 1085, 305, 33, 1, 255, 2314, 5768, 5719, 2545, 512, 42, 1, 511, 5899, 19261, 25994, 16661, 5285, 805, 52, 1, 1023, 14604, 60337, 106009, 92008, 41881, 10038, 1204, 63, 1

Offset: 0

Author

Paul Barry, Apr 01 2011

Keywords

• nonn
• tabl
• easy

Comments

First column is A000225. Row sums are A128714(n+2). Diagonal sums are A188464.

Examples

			Triangle begins
1,
3, 1,
7, 7, 1,
15, 30, 12, 1,
31, 103, 79, 18, 1,
63, 312, 387, 166, 25, 1,
127, 873, 1586, 1085, 305, 33, 1,
255, 2314, 5768, 5719, 2545, 512, 42, 1,
511, 5899, 19261, 25994, 16661, 5285, 805, 52, 1
		

Crossrefs

Cf. A119308.

Formula

G.f.: ((x-1)*sqrt(x^2*(y^2+4)-2*x*(y+2)+1)+x^2*(2-y)-x*(y+3)+1)/(2*x^3*y*(1+y-x)).