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A005437
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Column of Kempner tableau.
(Formerly M1276)
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5
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1, 1, 1, 2, 4, 14, 46, 224, 1024, 6320, 36976, 275792, 1965664, 17180144, 144361456, 1446351104, 13997185024, 158116017920, 1731678144256, 21771730437632, 266182076161024, 3686171162253824, 49763143319190016, 752594181757712384, 11118629668610842624
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OFFSET
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0,4
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COMMENTS
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Also the central column of the Seidel-Entringer triangles A008281 and A008282.
a(n) takes alternatingly the values of the central column of the Seidel-Entriger triangles A008281 (1,1,4,46,...) and A008282 (1,2,14,224,..).
In Gelineau, Shin, and Zeng (section 6.1) twelve interpretations of the numbers can be found. (End)
This sequence is the central sequence of numbers in the following table:
A_0 1
B_1 1 0
A_2 0 1 1
B_3 2 2 1 0
A_4 0 2 4 5 5
B_5 16 16 14 10 5 0
A_6 0 16 32 46 56 61 61
B_7 272 272 256 224 178 122 61 0
where row A_k is obtained from row B_(k-1) by the sequence 0, b_1, b_1+b_2, ..., b_1+b_2+....+b_k and row B_k is obtained from the row A_(k-1) by the sequence a_1+a_2+....+a_k, ..., a_(k-1)+a_k, a_k, 0. - Sean A. Irvine, Jun 25 2016
Named after the English-American mathematician Aubrey John Kempner (1880-1973). - Amiram Eldar, Jun 23 2021
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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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MAPLE
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A005437 := proc(n) local S; S := proc(n, k) option remember; if k=0 then `if`(n=0, 1, 0) else S(n, k-1)+S(n-1, n-k) fi end: S(n, iquo(n+1, 2)) end; seq(A005437(i), i=0..24); # Peter Luschny, Jul 09 2012
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MATHEMATICA
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a[n_] := Module[{S}, S[m_, k_] := S[m, k] = If[k == 0, If[m == 0, 1, 0], S[m, k-1] + S[m-1, m-k]]; S[n, Quotient[n+1, 2]]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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