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Search: id:A122848
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| A122848 |
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Exponential Riordan array (1,x(1+x/2)). |
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+0
3
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| 1, 0, 1, 0, 1, 1, 0, 0, 3, 1, 0, 0, 3, 6, 1, 0, 0, 0, 15, 10, 1, 0, 0, 0, 15, 45, 15, 1, 0, 0, 0, 0, 105, 105, 21, 1, 0, 0, 0, 0, 105, 420, 210, 28, 1, 0, 0, 0, 0, 0, 945, 1260, 378, 36, 1, 0, 0, 0, 0, 0, 945, 4725, 3150, 630, 45, 1, 0, 0, 0, 0, 0, 0, 10395, 17325, 6930, 990, 55, 1, 0, 0
(list; table; graph; listen)
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OFFSET
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0,9
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COMMENT
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Entries are Bessel polynomial coefficients. Row sums are A000085. Diagonal sums are A122849. Inverse is A122850. Product of A007318 and A122848 gives A100862.
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FORMULA
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Number triangle T(n,k)=k!*C(n,k)/((2k-n)!*2^(n-k))
T(n,k)=A001498(k,n-k) - Michael Somos Oct 03 2006
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EXAMPLE
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Triangle begins
1,
0, 1,
0, 1, 1,
0, 0, 3, 1,
0, 0, 3, 6, 1,
0, 0, 0, 15, 10, 1,
0, 0, 0, 15, 45, 15, 1,
0, 0, 0, 0, 105, 105, 21, 1
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PROGRAM
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(PARI) {T(n, k)=if(2*k<n|k>n, 0, n!/(2*k-n)!/(n-k)!*2^(k-n))} /* Michael Somos Oct 03 2006 */
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CROSSREFS
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Cf. A001497, A049403, A111924.
Sequence in context: A027200 A035654 A085604 this_sequence A054548 A059202 A058865
Adjacent sequences: A122845 A122846 A122847 this_sequence A122849 A122850 A122851
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 14 2006
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