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A115141
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Convolution of A115140 with itself.
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4
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1, -2, -1, -2, -5, -14, -42, -132, -429, -1430, -4862, -16796, -58786, -208012, -742900, -2674440, -9694845, -35357670, -129644790, -477638700, -1767263190, -6564120420, -24466267020, -91482563640, -343059613650, -1289904147324, -4861946401452, -18367353072152
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| This is the so-called A-sequence for the Riordan triangle A158454, as well as for A129818. For the notion of Z- and A-sequences for Riordan arrays see the W. Lang link under A006232 with details and references. W. Lang, Dec 20 1010.
a(n)*(-1)^n is the A-sequence for the Riordan triangle A111125. - From Wolfdieter Lang, Jun 26 2011.
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FORMULA
| O.g.f.: 1/c(x)^2 = (1-x) - x*c(x) with the o.g.f. c(x):=(1-sqrt(1-4*x))/(2*x) of A000108 (Catalan numbers).
a(0)=1, a(1)=-2, a(n)=-C(n-1), n>=2, with C(n):=A000108(n) (Catalan). The start [1, -2] is row n=2 of signed A034807 (signed Lucas polynomials). See A115149 and A034807 for comments.
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MATHEMATICA
| a[n_] := -First[ ListConvolve[ cc = Array[ CatalanNumber, n-1, 0], cc]]; a[0] = 1; a[1] = -2; Table[a[n], {n, 0, 27}] (* From Jean-François Alcover, Oct 21 2011 *)
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CROSSREFS
| Sequence in context: A117715 A160457 A107087 * A031148 A032238 A000619
Adjacent sequences: A115138 A115139 A115140 * A115142 A115143 A115144
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KEYWORD
| sign,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jan 13 2006
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