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A335647
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a(n) = binomial(4*n+1,n+1).
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0
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1, 10, 84, 715, 6188, 54264, 480700, 4292145, 38567100, 348330136, 3159461968, 28760021745, 262596783764, 2403979904200, 22057981462440, 202802465047245, 1867897112363100, 17231414395464984, 159186450151978480, 1472474663905800940, 13636219405675529520
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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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G.f. A(x)=x*B'(x)/B(x)+x*(1/x-1/(B(x))', B(x)=x(1+B(x))^4.
a(n) = Sum_{k=0..n+1} C(n+1,k)*C(3*n,k).
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PROG
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(Maxima)
a(n):=sum(binomial(n+1, k)*binomial(3*n, k), k, 0, n+1);
(PARI) a(n) = binomial(4*n+1, n+1); \\ Michel Marcus, Jun 15 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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