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A155161
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Triangle T(n,k), 0<=k<=n, read by rows given by [0,1,1,-1,0,0,0,0,0,0,0,...] DELTA [1,0,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 .
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11
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1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 3, 5, 3, 1, 0, 5, 10, 9, 4, 1, 0, 8, 20, 22, 14, 5, 1, 0, 13, 38, 51, 40, 20, 6, 1, 0, 21, 71, 111, 105, 65, 27, 7, 1, 0, 34, 130, 233, 256, 190, 98, 35, 8, 1, 0, 55, 235, 474, 594, 511, 315, 140, 44, 9, 1, 0, 89, 420, 942, 1324, 1295, 924, 490, 192
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| A Fibonacci convolution triangle ; Riordan array (1,x/(1-x-x^2)) .
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FORMULA
| a(n,k) = sum(M(k,i)*binomial(i,n-i-k),i,0,n-k), where M(n,k) = n(n+1)(n+2)...(n+k-1)/k! [Emanuele Munarini, Mar 15 2011]
Recurrence: a(n+2,k+1) = a(n+1,k+1) + a(n+1,k) + a(n,k+1) [Emanuele Munarini, Mar 15 2011]
G.f.: (1-x-x^2)/(1-x-x^2-x*y). - DELEHAM Philippe, Feb 08 2012
Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A141682(n+1), A052991(n), A155179(n), A155181(n), A155195(n), A155196(n), A155197(n), A155198(n), A155199(n) for x = 0,1,2,3,4,5,6,7,8,9 respectively. - DELEHAM Philippe, Feb 08 2012
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EXAMPLE
| Triangle begins : 1 ; 0,1 ; 0,1,1 ; 0,2,2,1 ; 0,3,5,3,1 ; 0,5,10,9,4,1 ; ...
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PROG
| (Maxima) M(n, k):=pochhammer(n, k)/k!;
create_list(sum(M(k, i)*binomial(i, n-i-k), i, 0, n-k), n, 0, 8, k, 0, n); [Emanuele Munarini, Mar 15 2011]
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CROSSREFS
| Cf. A000045, A037027
Sequence in context: A146527 A063250 A107424 * A185937 A065177 A064044
Adjacent sequences: A155158 A155159 A155160 * A155162 A155163 A155164
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KEYWORD
| nonn,tabl,changed
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 21 2009
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