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A132005
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Triangle, read by rows, where T(n,k) = n*T(n-1,k-1) + T(n-1,k-2) for n>0 and k>1, with T(n,0) = T(n-1,n-1) and T(n,1) = n*T(n-1,0) for n>0 and T(0,0) = 1.
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1
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1, 1, 1, 1, 2, 3, 3, 3, 7, 11, 11, 12, 15, 31, 51, 51, 55, 71, 87, 170, 286, 286, 306, 381, 481, 593, 1107, 1886, 1886, 2002, 2428, 2973, 3748, 4632, 8342, 14309, 14309, 15088, 17902, 21426, 26212, 32957, 40804, 71368, 122814, 122814, 128781, 150101, 176206
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums yield factorials (A000142).
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EXAMPLE
| Triangle begins:
1;
1, 1;
1, 2, 3;
3, 3, 7, 11;
11, 12, 15, 31, 51;
51, 55, 71, 87, 170, 286;
286, 306, 381, 481, 593, 1107, 1886;
1886, 2002, 2428, 2973, 3748, 4632, 8342, 14309;
14309, 15088, 17902, 21426, 26212, 32957, 40804, 71368, 122814;
122814, 128781, 150101, 176206, 210736, 257334, 322825, 400193, 683116, 1176694; ...
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PROG
| (PARI) {T(n, k)=if(k<0|n<k, 0, if(n==0&k==0, 1, if(k==0, T(n-1, n-1), n*T(n-1, k-1)+T(n-1, k-2))))}
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CROSSREFS
| Cf. A132006 (column 0).
Sequence in context: A141479 A055081 A109833 * A088041 A199457 A022296
Adjacent sequences: A132002 A132003 A132004 * A132006 A132007 A132008
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 07 2007
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