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A014327
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Convolution of Bell and Catalan numbers.
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1
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1, 2, 5, 14, 43, 143, 512, 1974, 8226, 37224, 183456, 984098, 5719900, 35767592, 238720688, 1688044543, 12568879291, 98065500372, 798734909795, 6771216844711, 59602783525634, 543665320690323, 5129940111134397, 49997388546860666, 502624275694700979
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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FORMULA
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From _G. C. Greubel_, Jan 08 2023: (Start)
G.f.: (1/(2*x))*(1 - sqrt(1-4*x))*Sum_{j>=0} A000110(j)*x^j. (End)
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MATHEMATICA
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A014327[n_]:= A014327[n]= Sum[BellB[j]*CatalanNumber[n-j], {j, 0, n}];
Table[A014327[n], {n, 0, 40}] (* _G. C. Greubel_, Jan 08 2023 *)
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PROG
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(Magma)
A014327:= func< n | (&+[Bell(j)*Catalan(n-j): j in [0..n]]) >;
[A014327(n): n in [0..40]]; // _G. C. Greubel_, Jan 08 2023
(SageMath)
def A014327(n): return sum(bell_number(j)*catalan_number(n-j) for j in range(n+1))
[A014327(n) for n in range(41)] # _G. C. Greubel_, Jan 08 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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_N. J. A. Sloane_
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STATUS
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approved
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