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A117178
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Riordan array (c(x^2)/sqrt(1-4x^2),xc(x^2)), c(x) the g.f. of A000108.
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1
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1, 0, 1, 3, 0, 1, 0, 4, 0, 1, 10, 0, 5, 0, 1, 0, 15, 0, 6, 0, 1, 35, 0, 21, 0, 7, 0, 1, 0, 56, 0, 28, 0, 8, 0, 1, 126, 0, 84, 0, 36, 0, 9, 0, 1, 0, 210, 0, 120, 0, 45, 0, 10, 0, 1, 462, 0, 330, 0, 165, 0, 55, 0, 11, 0, 1, 0, 792, 0, 495, 0, 220, 0, 66, 0, 12, 0, 1, 1716, 0, 1287, 0, 715, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Row sums are A058622(n+1). Diagonal sums are A001791(n+1), with interpolated zeros. Inverse is A117179.
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FORMULA
| Number triangle T(n,k)=C(n+1,(n-k)/2)(1+(-1)^(n-k))/2; Column k has e.g.f. Bessel_I(k,2x)+Bessel_I(k+2,2x).
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EXAMPLE
| Triangle begins
1,
0, 1,
3, 0, 1,
0, 4, 0, 1,
10, 0, 5, 0, 1,
0, 15, 0, 6, 0, 1,
35, 0, 21, 0, 7, 0, 1,
0, 56, 0, 28, 0, 8, 0, 1,
126,0, 84, 0, 36, 0, 9, 0, 1
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CROSSREFS
| Sequence in context: A049769 A117179 A111526 * A111527 A035695 A100257
Adjacent sequences: A117175 A117176 A117177 * A117179 A117180 A117181
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 01 2006
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