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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
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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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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):
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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];
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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) );
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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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