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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
 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 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.)