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A155112
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Triangle T(n,k), 0<=k<=n, read by rows given by [0,2,-1/2,-1/2,0,0,0,0,0,0,0,0,...]DELTA[1,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 .
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1
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1, 0, 1, 0, 2, 1, 0, 3, 4, 1, 0, 5, 10, 6, 1, 0, 8, 22, 21, 8, 1, 0, 13, 45, 59, 36, 10, 1, 0, 21, 88, 147, 124, 55, 12, 1, 0, 34, 167, 339, 366, 225, 78, 14, 1, 0, 55, 310, 741, 976, 770, 370, 105, 16, 1, 0, 89, 566, 1557, 2422, 2327, 1442, 567, 136, 18, 1, 0, 144, 1020, 3174
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| A Fibonacci convolution triangle ; Riordan array (1,x(1+x)/(1-x-x^2)).
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FORMULA
| Sum_{k, 0<=k<=n}T(n,k)*x^(n-k) = A000012(n), A155020(n), A154964(n), A154968(n), A154996(n), A154997(n), A154999(n), A155000(n), A155001(n), A155017(n) for x = 0,1,2,3,4,5,6,7,8,9 respectively .
Recurrence: T(n+2,k+1) = T(n+1,k+1) + T(n+1,k) + T(n,k+1) + T(n,k)
Explicit formula: T(n,k) = sum_{i=0}^{n/2} binomial(n-i,i)*binomial(n-i,k)*k/(n-i), for n > 0
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EXAMPLE
| Triangle begins : 1 ; 0,1 ; 0,2,1 ; 0,3,4,1 ; 0,5,10,6,1 ;...
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CROSSREFS
| Cf. A000045, A154929
Sequence in context: A193401 A095884 A128908 * A188286 A101603 A124030
Adjacent sequences: A155109 A155110 A155111 * A155113 A155114 A155115
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KEYWORD
| nonn,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 20 2009
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