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A104675
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a(n) = C(n+1,n) * C(n+6,1).
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2
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6, 14, 24, 36, 50, 66, 84, 104, 126, 150, 176, 204, 234, 266, 300, 336, 374, 414, 456, 500, 546, 594, 644, 696, 750, 806, 864, 924, 986, 1050, 1116, 1184, 1254, 1326, 1400, 1476, 1554, 1634, 1716, 1800, 1886, 1974, 2064, 2156, 2250, 2346, 2444, 2544, 2646
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: 2*(3 - 2*x) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2.
(End)
Sum_{n>=0} 1/a(n) = 137/300.
Sum_{n>=0} (-1)^n/a(n) = 2*log(2)/5 - 47/300. (End)
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EXAMPLE
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If n=0 then C(0+1,0+0) * C(0+6,1) = C(1,0) * C(6,1) = 1*6 = 6.
If n=5 then C(5+1,5+0) * C(5+6,1) = C(6,5) * C(11,1) = 6*11 = 66.
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MATHEMATICA
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Table[Binomial[n + 1, n] Binomial[n + 6, 1], {n, 0, 48}] (* or *)
CoefficientList[Series[2 (3 - 2 x)/(1 - x)^3, {x, 0, 49}], x] (* or *)
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PROG
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(PARI) Vec(2*(3 - 2*x) / (1 - x)^3 + O(x^80)) \\ Colin Barker, Apr 06 2017
(Python)
from sympy import binomial
def a(n): return binomial(n + 1, n) * binomial(n + 6, 1) # Indranil Ghosh, Apr 06 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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