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A232774 Triangle T(n,k), read by rows, given by : T(n,0)=1, T(n,1)=2^(n+1)-n-2, T(n,n)=(-1)^(n-1) for n>0, T(n,k)=T(n-1,k)-T(n-1,k-1) for 1<k<n. 0
1, 1, 1, 1, 4, -1, 1, 11, -5, 1, 1, 26, -16, 6, -1, 1, 57, -42, 22, -7, 1, 1, 120, -99, 64, -29, 8, -1, 1, 247, -219, 163, -93, 37, -9, 1, 1, 502, -466, 382, -256, 130, -46, 10, -1, 1, 1013, -968, 848, -638, 386, -176, 56, -11, 1, 2036, -1981, 1816, -1486, 1024 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are A000079(n)=2^n.

Diagonal sums are A024493(n+1)=A130781(n).

Sum_{k=0..n} T(n,k)*x^k = -A003063(n+2), A159964(n), A000012(n), A000079(n), A001045(n+2), A164906(n), (-1)^(n+1)*A232015(n+1) for x = -2, -1, 0, 1, 2, 3, 4 respectively.

LINKS

Table of n, a(n) for n=0..59.

FORMULA

G.f.: Sum_{x>=0, k=0..n} y^k*x^n=(1+2*(y-1)*x)/((1-2*x)*(1+(y-1)*x)).

|T(2*n,n)|=4^n=A000302(n).

EXAMPLE

Triangle begins:

1

1, 1

1, 4, -1

1, 11, -5, 1

1, 26, -16, 6, -1

1, 57, -42, 22, -7, 1

1, 120, -99, 64, -29, 8, -1

1, 247, -219, 163, -93, 37, -9, 1

1, 502, -466, 382, -256, 130, -46, 10, -1

1, 1013, -968, 848, -638, 386, -176, 56, -11, 1

CROSSREFS

Columns: A000012, A000295, -A002662, A002663, -A002664, A035038, -A035039, A035040, -A035041, A035042

Cf. A055248

Sequence in context: A261762 A225062 A145271 * A203860 A147564 A090981

Adjacent sequences:  A232771 A232772 A232773 * A232775 A232776 A232777

KEYWORD

sign,tabl

AUTHOR

Philippe Deléham, Nov 30 2013

STATUS

approved

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Last modified March 24 12:14 EDT 2019. Contains 321448 sequences. (Running on oeis4.)