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A156644 Mirror image of triangle A080233. 5
1, 0, 1, -1, 1, 1, -2, 0, 2, 1, -3, -2, 2, 3, 1, -4, -5, 0, 5, 4, 1, -5, -9, -5, 5, 9, 5, 1, -6, -14, -14, 0, 14, 14, 6, 1, -7, -20, -28, -14, 14, 28, 20, 7, 1, -8, -27, -48, -42, 0, 42, 48, 27, 8, 1, -9, -35, -75, -90, -42, 42, 90, 75, 35, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

Inverse of A239473. Equals A007318*A167374. - Tom Copeland, Nov 14 2016

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(n,k)=A080233(n,n-k) = (-1)^(n-k)*A097808(n,k) . T(n,k)=binomial(n,k)*(2*k-n+1)/(k+1). T(n,k)=T(n-1,k-1)+T(n-1,k), k>0 ; T(n,0)=1-n=A024000(n), T(n,n)=1.

T(n,k) = binomial(n,k) - binomial(n,k+1) = sum_{i=-k-1..k+1} (-1)^(i+1) * binomial(n,k+1+i) * binomial(n+2,k+1-i). - Mircea Merca, Apr 28 2012

EXAMPLE

Triangle begins: 1 ; 0,1 ; -1,1,1 ; -2,0,2,1 ; -3,-2,2,3,1 ; -4,-5,0,5,4,1 ; ...

MATHEMATICA

Table[Binomial[n, k] - Binomial[n, k + 1], {n, 0, 10}, {k, 0, n}] // Flatten (* Michael De Vlieger, Nov 24 2016 *)

CROSSREFS

Cf. A080956, A120730.

Cf. A007318, A167374, A239473.

Sequence in context: A265753 A138110 A080233 * A097808 A114325 A101048

Adjacent sequences:  A156641 A156642 A156643 * A156645 A156646 A156647

KEYWORD

sign,tabl

AUTHOR

Philippe Deléham, Feb 12 2009

STATUS

approved

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Last modified January 23 12:31 EST 2021. Contains 340385 sequences. (Running on oeis4.)