A177977 Triangle read by rows. Polynomials based on sums of Moebius transforms.

1, 1, 0, 1, 3, -2, 1, 6, 5, -6, 1, 10, 35, 26, -48, 1, 15, 85, 165, -26, -120, 1, 21, 175, 735, 1264, -36, -1440, 1, 28, 322, 1960, 5929, 8092, -1212, -10080, 1, 36, 546, 4536, 22449, 60564, 57644, -24816, -80640, 1, 45, 870, 9450, 63273, 254205, 572480

Offset

1,5

Comments

These polynomials were found by entering the rows of A177976 in Wolfram Alpha. The lower left half equals part of the Stirling numbers of the first kind given in table A094638. To evaluate, enter a value for n and divide row sums with factorial numbers as shown in the example section. n=-1 gives A092149, n=0 gives the Mertens function A002321, n=1 gives A000012, n=2 gives A002088, n=3 gives A015631, and n=4 gives A015634.

Links

Table of n, a(n) for n=1..52.

Example

Triangle begins and the polynomials are:
(1*n^0)/1
(1*n^1 +0*n^0)/1
(1*n^2 +3*n^1 -2*n^0)/2
(1*n^3 +6*n^2 +5*n^1 -6*n^0)/6
(1*n^4 +10*n^3 +35*n^2 +26*n^1 -48*n^0)/24
(1*n^5 +15*n^4 +85*n^3 +165*n^2 -26*n^1 -120*n^0)/120
(1*n^6 +21*n^5 +175*n^4 +735*n^3 +1264*n^2 -36*n^1 -1440*n^0)/720

Crossrefs

Sequence in context: A115094 A165958 A113655 * A365743 A208520 A114155

Adjacent sequences: A177974 A177975 A177976 * A177978 A177979 A177980

Keyword

sign,tabl

Author

Mats Granvik, May 16 2010

Extensions

Typo in sequence (erroneous comma) corrected by N. J. A. Sloane, May 22 2010

Status

approved