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A007044
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Left diagonal of partition triangle A047812.
(Formerly M4370)
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4
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0, 0, 1, 7, 20, 48, 100, 194, 352, 615, 1034, 1693, 2705, 4239, 6522, 9889, 14786, 21844, 31913, 46165, 66162, 94035, 132600, 185637, 258128, 356674, 489906, 669173, 909212, 1229217, 1653993, 2215597, 2955192, 3925659, 5194520, 6847963, 8995524, 11776227
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,4
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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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Alois P. Heinz, Table of n, a(n) for n = 1..500
R. K. Guy, Letter to N. J. A. Sloane, Aug. 1992
R. K. Guy, Parker's permutation problem involves the Catalan numbers, Preprint, 1992. (Annotated scanned copy)
R. K. Guy, Parker's permutation problem involves the Catalan numbers, Amer. Math. Monthly 100 (1993), 287-289.
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MAPLE
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b:= proc(n, i, t) option remember; `if`(n=0, 1, `if`(n<0
or t*i<n, 0, b(n, i-1, t)+b(n-i, min(i, n-i), t-1)))
end:
a:= n-> b(2*n+2, n$2):
seq(a(n), n=1..50); # Alois P. Heinz, May 31 2020
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MATHEMATICA
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b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, If[n < 0 || t i < n, 0, b[n, i - 1, t] + b[n - i, Min[i, n - i], t - 1]]];
a[n_] := b[2n+2, n, n];
Array[a, 50] (* Jean-François Alcover, Nov 23 2020, after Alois P. Heinz *)
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PROG
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(PARI) T(n, k) = polcoeff(prod(j=0, n-1, (1-q^(2*n-j))/(1-q^(j+1)) ), k*(n+1) );
for(n=1, 40, print1(T(n, 2), ", ")) \\ Petros Hadjicostas, May 31 2020
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CROSSREFS
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Cf. A007042, A007045, A047812, A051643.
Sequence in context: A100206 A298288 A299384 * A047862 A264879 A320681
Adjacent sequences: A007041 A007042 A007043 * A007045 A007046 A007047
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane and R. K. Guy
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EXTENSIONS
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Name edited by Petros Hadjicostas, May 31 2020
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STATUS
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approved
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