A105847 - OEIS

A105847

Inverse binomial transform of number triangle A105632.

1, 0, 1, 1, -1, 1, 0, 3, -2, 1, 2, -3, 6, -3, 1, 0, 9, -10, 10, -4, 1, 5, -9, 26, -22, 15, -5, 1, 0, 29, -42, 59, -40, 21, -6, 1, 14, -29, 108, -121, 115, -65, 28, -7, 1, 0, 99, -174, 308, -276, 202, -98, 36, -8, 1, 42, -99, 450, -620, 734, -546, 329, -140, 45, -9, 1, 0, 351, -726, 1547, -1700, 1540, -980, 506, -192, 55, -10, 1, 132

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OFFSET

0,8

COMMENTS

Product of Riordan array (1/(1+x),x/(1+x)) (inverse binomial matrix) and A105632. Rows sums are A007477.

LINKS

Table of n, a(n) for n=0..78.

FORMULA

Column k has g.f. (sum{j=0..k-1, C(k-1, j)C(j)x^(2j)/(1-4x^2)^(j+1/2)}+0^k*(1-sqrt(1-4x^2))/(2x^2))(x/(1+x))^k

EXAMPLE

Triangle begins

0,1;

1,-1,1;

0,3,-2,1;

2,-3,6,-3,1;

0,9,-10,10,-4,1;

CROSSREFS

Sequence in context: A232191 A183041 A136560 * A240485 A048984 A329587

Adjacent sequences: A105844 A105845 A105846 * A105848 A105849 A105850

KEYWORD

easy,sign,tabl

AUTHOR

Paul Barry, Apr 22 2005

STATUS

approved