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

0,2

Comments

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

Links

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

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)).

Example

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.

Sequence in context: A322753 A136035 A132307 * A369892 A359576 A319298

Adjacent sequences: A188460 A188461 A188462 * A188464 A188465 A188466

Keyword

nonn,tabl,easy

Author

Paul Barry, Apr 01 2011

Status

approved