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A136397 Triangle read by rows of coefficients of Chebyshev-like polynomials P_{n,5}(x) with 0 omitted (exponents in increasing order). 0
1, -5, 2, 10, -11, 4, -10, 25, -24, 8, 5, -30, 61, -52, 16, -1, 20, -85, 146, -112, 32, -7, 70, -231, 344, -240, 64, 1, -34, 225, -608, 800, -512, 128, 9, -138, 681, -1560, 1840, -1088, 256, -1, 52, -501, 1970, -3920, 4192, -2304, 512 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

COMMENTS

If U_n(x), T_n(x) are Chebyshev's polynomials then U_n(x)=P_{n,0}(x), T_n(x)=P_{n,1}(x).

Let n>=5 and k be of the same parity. Consider a set X consisting of (n+k)/2-5 blocks of the size 2 and an additional block of the size 5, then (-1)^((n-k)/2)a(n,k) is the number of n-5-subsets of X intersecting each block of the size 2.

LINKS

Table of n, a(n) for n=5..53.

Milan Janjic, Two enumerative functions.

M. Janjic, On a class of polynomials with integer coefficients, JIS 11 (2008) 08.5.2

FORMULA

If n>=5 and k are of the same parity then a(n,k)= (-1)^((n-k)/2)*sum((-1)^i*binomial((n+k)/2-5, i)*binomial(n+k-5-2*i, n-5), i=0..(n+k)/2-5) and a(n,k)=0 if n and k are of different parity.

EXAMPLE

Rows are (1),(-5,2),(10,-11,4),... since P_{5,5}=x^5, P_{6,5}=-5x^4+2x^6, P_{7,5}=10x^3-11x^5+4x^7,...

MAPLE

if modp(n-k, 2)=0 then a[n, k]:=(-1)^((n-k)/2)*sum((-1)^i*binomial((n+k)/2-5, i)*binomial(n+k-5-2*i, n-5), i=0..(n+k)/2-5); end if;

CROSSREFS

Cf. A008310, A053117.

Sequence in context: A249368 A055682 A187875 * A065292 A090812 A050004

Adjacent sequences:  A136394 A136395 A136396 * A136398 A136399 A136400

KEYWORD

sign,tabf

AUTHOR

Milan Janjic, Mar 30 2008, revised Apr 05 2008

STATUS

approved

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Last modified December 4 21:33 EST 2016. Contains 278755 sequences.