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Search: id:A132007
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| A132007 |
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Triangle, read by rows, where T(n,k) = T(n,k-1) + n*T(n-1,k-1) for n>0 and k>0, with T(n,0) = T(n-1,n-1) for n>0 and T(0,0) = 1. |
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+0
2
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| 1, 1, 2, 2, 4, 8, 8, 14, 26, 50, 50, 82, 138, 242, 442, 442, 692, 1102, 1792, 3002, 5212, 5212, 7864, 12016, 18628, 29380, 47392, 78664, 78664, 115148, 170196, 254308, 384704, 590364, 922108, 1472756, 1472756, 2102068, 3023252, 4384820, 6419284
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Column 0 and main diagonal (offset) equals A110083.
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FORMULA
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T(n+1,0) = Sum_{k=0..n} (n!/k!)*C(n,k)*T(k,0) for n>=0 with T(0,0)=1.
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EXAMPLE
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Triangle begins:
1;
1, 2;
2, 4, 8;
8, 14, 26, 50;
50, 82, 138, 242, 442;
442, 692, 1102, 1792, 3002, 5212;
5212, 7864, 12016, 18628, 29380, 47392, 78664;
78664, 115148, 170196, 254308, 384704, 590364, 922108, 1472756;
1472756, 2102068, 3023252, 4384820, 6419284, 9496916, 14219828, 21596692, 33378740; ...
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PROGRAM
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(PARI) {T(n, k)=if(k<0|n<k, 0, if(n==0&k==0, 1, if(k==0, T(n-1, n-1), T(n, k-1)+n*T(n-1, k-1))))}
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CROSSREFS
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Cf. A110083 (column 0); A132008 (row sums).
Sequence in context: A048572 A121173 A101651 this_sequence A094605 A085619 A085620
Adjacent sequences: A132004 A132005 A132006 this_sequence A132008 A132009 A132010
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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), Aug 07 2007
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