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A034789
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Related to sextic factorial numbers A008542.
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2
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1, 21, 546, 15561, 466830, 14471730, 458960580, 14801478705, 483514971030, 15955994043990, 530899438190940, 17785131179396490, 599222112044281740, 20287948650642110340, 689790254121831751560, 23539092421907508521985
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: (-1+(1-36*x)^(-1/6))/6.
D-finite with recurrence: n*a(n) +6*(-6*n+5)*a(n-1)=0. - R. J. Mathar, Jan 28 2020
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MAPLE
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seq( 6^(n-1)*mul(6*j-5, j=1..n)/n!, n=1..20); # G. C. Greubel, Nov 11 2019
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MATHEMATICA
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Rest@ CoefficientList[Series[(-1 + (1 - 36 x)^(-1/6))/6, {x, 0, 16}], x] (* Michael De Vlieger, Oct 13 2019 *)
Table[6^(2*n-1)*Pochhammer[1/6, n]/n!, {n, 20}] (* G. C. Greubel, Nov 11 2019 *)
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PROG
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(PARI) vector(20, n, 6^(n-1)*prod(j=1, n, 6*j-5)/n! ) \\ G. C. Greubel, Nov 11 2019
(Magma) [6^(n-1)*(&*[6*j-5: j in [1..n]])/Factorial(n): n in [1..20]]; // G. C. Greubel, Nov 11 2019
(Sage) [6^(n-1)*product( (6*j-5) for j in (1..n))/factorial(n) for n in (1..20)] # G. C. Greubel, Nov 11 2019
(GAP) List([1..20], n-> 6^(n-1)*Product([1..n], j-> 6*j-5)/Factorial(n) ); # G. C. Greubel, Nov 11 2019
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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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