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Search: id:A101494
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| A101494 |
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Triangle, read by rows, where T(n,k) = Sum_{j=0..n-k-1} C(j+k,j)*T(n-1,j+k) for n>k>=0 with T(n,n)=1. |
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+0
2
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| 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 9, 8, 4, 1, 1, 23, 23, 13, 5, 1, 1, 66, 73, 44, 19, 6, 1, 1, 210, 253, 162, 73, 26, 7, 1, 1, 733, 948, 643, 302, 111, 34, 8, 1, 1, 2781, 3817, 2724, 1337, 506, 159, 43, 9, 1, 1, 11378, 16433, 12259, 6266, 2457, 788, 218, 53, 10, 1, 1, 49864, 75295
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Column 0 equals row sums (A026898) shift right.
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FORMULA
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T(n, 0) = Sum_{k=0..n} (n-k+1)^k = A026898(n).
T(n,k) = Sum_{j=0..n-k} binomial(j+k,j)*(n-k-j)^j. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 07 2006
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EXAMPLE
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4-th row sum = 23 = (5-0)^0+(5-1)^1+(5-2)^2+(5-3)^3+(5-4)^4.
5-th row sum = 66 = (6-0)^0+(6-1)^1+(6-2)^2+(6-3)^3+(6-4)^4+(6-5)^5.
T(6,0) = 66 = 1*23 + 1*23 + 1*13 + 1*5 + 1*1 + 1*1.
T(6,1) = 73 = 1*23 + 2*13 + 3*5 + 4*1 + 5*1.
T(6,2) = 44 = 1*13 + 3*5 + 6*1 + 10*1.
Rows begin:
[1],
[1,1],
[2,1,1],
[4,3,1,1],
[9,8,4,1,1],
[23,23,13,5,1,1],
[66,73,44,19,6,1,1],
[210,253,162,73,26,7,1,1],
[733,948,643,302,111,34,8,1,1],
[2781,3817,2724,1337,506,159,43,9,1,1],...
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PROGRAM
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(PARI) {T(n, k)=if(n<k|k<0, 0, if(n==k, 1, sum(j=0, n-k-1, binomial(j+k, j)*T(n-1, j+k)); ))}
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CROSSREFS
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Cf. A101495, A026898.
Sequence in context: A105632 A091491 A117418 this_sequence A125781 A091150 A091351
Adjacent sequences: A101491 A101492 A101493 this_sequence A101495 A101496 A101497
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jan 21 2005
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