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1, 1, 1, 1, 2, 3, 1, 3, 9, 7, 1, 4, 18, 28, 19, 1, 5, 30, 70, 95, 51, 1, 6, 45, 140, 285, 306, 141, 1, 7, 63, 245, 665, 1071, 987, 393, 1, 8, 84, 392, 1330, 2856, 3948, 3144, 1107, 1, 9, 108, 588, 2394, 6426, 11844, 14148, 9963, 3139
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Right border = A002426. Row sums = A000984: (1, 2, 6, 20, 70, 252,...).
The n-th row of this this triangle are the coefficients of the polynomial: p := 1/Pi*int((1+t-2*t*cos(s))^n, s=0..Pi); Pi / 1 | n p := ---- | (1 + t - 2 t cos(s)) ds Pi | / 0 for example n=5 then 4 2 3 p = 19 t + 18 t + 28 t + 4 t + 1 [From Theodore Kolokolnikov (tkolokol(AT)gmail.com), Oct 09 2010]
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FORMULA
| A007318 * triangle M, where M = A002426 * 0^(n-k), 0<=k<=n; i.e. M = an infinite lower triangular matrix with A002426 as the right border and the rest zeros.
O.g.f. appears to be
1/sqrt(1-t*(1-x))*1/sqrt(1-t*(1+3*x)) = 1+(1+x)*t+(1+2*x+3*x^2)*t^2+....
See A098473.
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EXAMPLE
| First few rows of the triangle are:
1;
1, 1;
1, 2, 3;
1, 3, 9, 7;
1, 4, 18, 28, 19;
1, 5, 30, 70, 95, 51;
1, 6, 45, 140, 285, 306, 141;
1, 7, 63, 245, 665, 1071, 987, 393;
...
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CROSSREFS
| Cf. A002426, A000984, A098473.
Sequence in context: A139633 A152440 A134319 * A171150 A111589 A010027
Adjacent sequences: A135088 A135089 A135090 * A135092 A135093 A135094
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 18 2007
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