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 A135091 A007318 * triangle M, where M = A002426 * 0^(n-k), 0<=k<=n. 3
 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; text; internal format)
 OFFSET 0,5 COMMENTS Right border = A002426. Row sums = A000984: (1, 2, 6, 20, 70, 252,...). The n-th row of 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, Oct 09 2010] LINKS 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. 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; ... CROSSREFS Cf. A002426, A000984, A098473. Sequence in context: A208330 A152440 A134319 * A171150 A111589 A259760 Adjacent sequences:  A135088 A135089 A135090 * A135092 A135093 A135094 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Nov 18 2007 STATUS approved

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Last modified October 20 15:46 EDT 2019. Contains 328267 sequences. (Running on oeis4.)