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A007472
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Shifts 2 places left when binomial transform is applied twice.
(Formerly M2812)
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12
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1, 1, 1, 3, 9, 29, 105, 431, 1969, 9785, 52145, 296155, 1787385, 11428949, 77124569, 546987143, 4062341601, 31502219889, 254500383457, 2137863653811, 18639586581097, 168387382189709, 1573599537048265, 15189509662516063, 151243491212611217, 1551565158004180137
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OFFSET
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0,4
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
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FORMULA
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G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - 2*x)) / (1 - 2*x). - Ilya Gutkovskiy, Jan 30 2022
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MAPLE
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bintr:= proc(p) local b;
b:=proc(n) option remember; add (p(k)*binomial(n, k), k=0..n) end
end:
b:= (bintr@@2)(a):
a:= n-> `if`(n<2, 1, b(n-2)):
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MATHEMATICA
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bintr[p_] := Module[{b}, b[n_] := b[n] = Sum [p[k]*Binomial[n, k], {k, 0, n}]; b]; b = a // bintr // bintr; a[n_] := If[n<2, 1, b[n-2]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jan 27 2014, after Alois P. Heinz *)
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CROSSREFS
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KEYWORD
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nonn,nice,eigen
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AUTHOR
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STATUS
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approved
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