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Search: id:A099755
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| A099755 |
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Triangle read by rows: T(n,0)=1, T(n,n)=(2*n-1)!!+1, T(m,n)=2*(m-n)*T(m-1,n-1)+(2*n+2)*T(m-1,n). |
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+0
1
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| 1, 1, 2, 1, 10, 4, 1, 44, 44, 16, 1, 182, 440, 216, 106, 1, 736, 3732, 3488, 1492, 946, 1, 2954, 28280, 50296, 28872, 14336, 10396, 1, 11828, 199220, 628608, 590496, 287520, 174216, 135136, 1, 47326, 1337256, 7021064, 10933824, 6993216, 3589104, 2510608
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OFFSET
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0,3
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FORMULA
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Sum(k=0..n: T(n, k))=(2*k+1)!! ==2*k+1)*(2*k-1)*(2*k-3)*...
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EXAMPLE
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Triangle begins:
1
1 2
1 10 4
1 44 44 16
1 182 440 216 106
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MAPLE
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T:=proc(n, k) if k=0 then 1 elif n=k then 1+(2*k)!/(k!*2^k) elif k>n then 0 else 2*(n-k)*T(n-1, k-1)+(2*k+2)*T(n-1, k) fi end: for n from 0 to 9 do [seq(T(n, k), k=0..n)] od;
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CROSSREFS
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Cf. A060187.
Sequence in context: A144275 A011268 A142963 this_sequence A110682 A110327 A105615
Adjacent sequences: A099752 A099753 A099754 this_sequence A099756 A099757 A099758
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Miklos Kristof (kristmikl(AT)freemail.hu), Nov 11 2004
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