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 A135356 Triangle T(p,s) read by rows: coefficients in the recurrence of sequences which equal their p-th differences. 12
 2, 2, 0, 3, -3, 2, 4, -6, 4, 0, 5, -10, 10, -5, 2, 6, -15, 20, -15, 6, 0, 7, -21, 35, -35, 21, -7, 2, 8, -28, 56, -70, 56, -28, 8, 0, 9, -36, 84, -126, 126, -84, 36, -9, 2, 10, -45, 120, -210, 252, -210, 120, -45, 10, 0, 11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sequences which equal their p-th differences obey recurrences a(n)=sum(s=1..p) T(p,s)*a(n-s). This defines T(p,s) as essentially a signed version of a chopped Pascal triangle A014410, see A130785. For cases like p=2, 4, 6, 8, 10, 12, 14, the denominator of the rational generating function of a(n) contains a factor 1-x; depending on the first terms in the sequences a(n), additional, simpler recurrences may exist if this cancels with a factor in the numerator. - R. J. Mathar, Jun 10 2008 Row sums are 2. LINKS Alois P. Heinz, Rows n = 1..141, flattened FORMULA T(p,s) = (-1)^(s+1)*A007318(p,s), 1<=s  `if`(p=s, 2*irem(p, 2), (-1)^(s+1) *binomial(p, s)): seq(seq(T(p, s), s=1..p), p=1..11);  # Alois P. Heinz, Aug 26 2011 MATHEMATICA T[p_, s_] := If[p == s, 2*Mod[s, 2], (-1)^(s+1)*Binomial[p, s]]; Table[T[p, s], {p, 1, 11}, {s, 1, p}] // Flatten (* Jean-François Alcover, Feb 19 2015, after Alois P. Heinz *) CROSSREFS Cf. A130785. Sequence in context: A048142 A071426 A288530 * A259016 A216504 A216673 Adjacent sequences:  A135353 A135354 A135355 * A135357 A135358 A135359 KEYWORD sign,tabl AUTHOR Paul Curtz, Dec 08 2007, Mar 25 2008, Apr 28 2008 EXTENSIONS Edited by R. J. Mathar, Jun 10 2008 STATUS approved

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