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A084610 Triangle, read by rows, where the n-th row lists the (2n+1) coefficients of (1+x-x^2)^n. 11
1, 1, 1, -1, 1, 2, -1, -2, 1, 1, 3, 0, -5, 0, 3, -1, 1, 4, 2, -8, -5, 8, 2, -4, 1, 1, 5, 5, -10, -15, 11, 15, -10, -5, 5, -1, 1, 6, 9, -10, -30, 6, 41, -6, -30, 10, 9, -6, 1, 1, 7, 14, -7, -49, -14, 77, 29, -77, -14, 49, -7, -14, 7, -1, 1, 8, 20, 0, -70, -56, 112, 120, -125, -120, 112, 56, -70, 0, 20, -8, 1, 1, 9, 27, 12, -90, -126, 126, 288 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Paul D. Hanna, Rows n=0..34 of triangle, flattened

FORMULA

G.f.: G(0)/2 , where G(k)= 1 + 1/( 1 - (1+x-x^2)*x^(2*k+1)/((1+x-x^2)*x^(2*k+1) + 1/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 06 2013

EXAMPLE

Rows:

{1},

{1,1,-1},

{1,2,-1,-2,1},

{1,3,0,-5,0,3,-1},

{1,4,2,-8,-5,8,2,-4,1},

{1,5,5,-10,-15,11,15,-10,-5,5,-1},

{1,6,9,-10,-30,6,41,-6,-30,10,9,-6,1},

{1,7,14,-7,-49,-14,77,29,-77,-14,49,-7,-14,7,-1},

PROG

(PARI) for(n=0, 12, for(k=0, 2*n, t=polcoeff((1+x-x^2)^n, k, x); print1(t", ")); print(" "))

CROSSREFS

Cf. A002426, A084600-A084609, A084611-A084615.

Sequence in context: A269329 A117166 A078996 * A303336 A129479 A261095

Adjacent sequences:  A084607 A084608 A084609 * A084611 A084612 A084613

KEYWORD

sign,tabf

AUTHOR

Paul D. Hanna, Jun 01 2003

STATUS

approved

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Last modified July 17 14:44 EDT 2019. Contains 325106 sequences. (Running on oeis4.)