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Search: id:A111062
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| A111062 |
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Triangle T(n, k), 0<=k<=n, defined by T(n, k) = binomial(n, k)*A000085(n-k). |
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3
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| 1, 1, 1, 2, 2, 1, 4, 6, 3, 1, 10, 16, 12, 4, 1, 26, 50, 40, 20, 5, 1, 76, 156, 150, 80, 30, 6, 1, 232, 532, 546, 350, 140, 42, 7, 1, 764, 1856, 2128, 1456, 700, 224, 56, 8, 1, 2620, 6876, 8352, 6384, 3276, 1260, 336, 72, 9, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Triangle related to A000085.
Riordan array [exp(x(2+x)/2),x]. [From Paul Barry (pbarry(AT)wit.ie), Nov 05 2008]
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FORMULA
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Sum_{k>=0} T(m, k)*T(n, k)*k! = T(m+n, 0) = A000085(m+n).
Sum_{k, 0<=k<=n} T(n, k) = A005425(n).
Apparently satisfies T(n,m) = T(n-1,m-1) + T(n-1,m) + m * T(n-1,m+1). - Franklin T. Adams-Watters, Dec 22 2005
T(n,k)=(n!/k!)sum{j=0..n-k, C(j,n-k-j)/(j!*2^(n-k-j))}; [From Paul Barry (pbarry(AT)wit.ie), Nov 05 2008]
G.f.: 1/(1-xy-x-x^2/(1-xy-x-2x^2/(1-xy-x-3x^2/(1-xy-x-4x^2/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Apr 23 2009]
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EXAMPLE
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Rows begin:
1;
1, 1;
2, 2, 1;
4, 6, 3, 1;
10, 16, 12, 4, 1;
26, 50, 40, 20, 5, 1;
76, 156, 150, 80, 30, 6, 1;
232, 532, 546, 350, 140, 42, 7, 1;
764, 1856, 2128, 1456, 700, 224, 56, 8, 1;
2620, 6876, 8352, 6384, 3276, 1260, 336, 72, 9, 1;
Contribution from Paul Barry (pbarry(AT)wit.ie), Apr 23 2009: (Start)
Production matrix is
1, 1,
1, 1, 1,
0, 2, 1, 1,
0, 0, 3, 1, 1,
0, 0, 0, 4, 1, 1,
0, 0, 0, 0, 5, 1, 1,
0, 0, 0, 0, 0, 6, 1, 1,
0, 0, 0, 0, 0, 0, 7, 1, 1,
0, 0, 0, 0, 0, 0, 0, 8, 1, 1 (End)
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CROSSREFS
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Cf. A000085, A007318, A005425 (row sums), A013989.
Sequence in context: A119468 A091869 A112307 this_sequence A061598 A071946 A053495
Adjacent sequences: A111059 A111060 A111061 this_sequence A111063 A111064 A111065
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 07 2005
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EXTENSIONS
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Corrected by Franklin T. Adams-Watters, Dec 22 2005
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