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Search: id:A117184
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| A117184 |
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Riordan array ((1+x)c(x^2)/sqrt(1-4x^2),xc(x^2)), c(x) the g.f. of A000108. |
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+0
4
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| 1, 1, 1, 3, 1, 1, 3, 4, 1, 1, 10, 4, 5, 1, 1, 10, 15, 5, 6, 1, 1, 35, 15, 21, 6, 7, 1, 1, 35, 56, 21, 28, 7, 8, 1, 1, 126, 56, 84, 28, 36, 8, 9, 1, 1, 126, 210, 84, 120, 36, 45, 9, 10, 1, 1, 462, 210, 330, 120, 165, 45, 55, 10, 11, 1, 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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Row sums are A117186. Diagonal sums are A117187. Inverse is A117185.
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FORMULA
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Number triangle T(n,k)=C(n+1,(n+k)/2+1)(1+(-1)^(n-k))/2+C(n,(n+k)/2+1/2)(1-(-1)^(n-k))/2; Column k has e.g.f. Bessel_I(k,2x)+Bessel_I(k+1,2x)+Bessel_I(k+2,2x).
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EXAMPLE
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Triangle begins
1,
1, 1,
3, 1, 1,
3, 4, 1, 1,
10, 4, 5, 1, 1,
10, 15, 5, 6, 1, 1,
35, 15, 21, 6, 7, 1, 1,
35, 56, 21, 28, 7, 8, 1, 1
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CROSSREFS
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Sequence in context: A059959 A051120 A114476 this_sequence A035690 A124794 A097560
Adjacent sequences: A117181 A117182 A117183 this_sequence A117185 A117186 A117187
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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), Mar 01 2006
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