A020070
a(n) = floor( Gamma(n+7/8)/Gamma(7/8) ).
Original entry on oeis.org
1, 0, 1, 4, 18, 89, 523, 3598, 28341, 251531, 2483877, 27012163, 320769440, 4129906548, 57302453360, 852373993744, 13531437150692, 228343001917931, 4081631159283027, 77040788131467135, 1531185664112909314
Offset: 0
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[Floor(Gamma(n+7/8)/Gamma(7/8)): n in [0..25]]; // G. C. Greubel, Nov 17 2019
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Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;
seq(floor(pochhammer(7/8,n)), n = 0..25); # G. C. Greubel, Nov 17 2019
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Floor[Pochhammer[7/8, Range[0, 25]]] (* G. C. Greubel, Nov 17 2019 *)
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vector(26, n, my(x=7/8); gamma(n-1+x)\gamma(x) ) \\ G. C. Greubel, Nov 17 2019
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[floor(rising_factorial(7/8, n)) for n in (0..25)] # G. C. Greubel, Nov 17 2019
A020071
a(n) = floor( Gamma(n+5/8)/Gamma(5/8) ).
Original entry on oeis.org
1, 0, 1, 2, 9, 44, 251, 1665, 12700, 109544, 1054363, 11202616, 130230419, 1644159040, 22401666926, 327624378797, 5119130918712, 85105551523594, 1499985345603353, 27937227061862467, 548268081089050917
Offset: 0
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[Floor(Gamma(n+5/8)/Gamma(5/8)): n in [0..25]]; // G. C. Greubel, Nov 17 2019
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Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;
seq(floor(pochhammer(5/8,n)), n = 0..25); # G. C. Greubel, Nov 17 2019
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Floor[Pochhammer[5/8, Range[0, 25]]] (* G. C. Greubel, Nov 17 2019 *)
Table[Floor[(Gamma[n+5/8])/Gamma[5/8]],{n,0,20}] (* Harvey P. Dale, Nov 24 2024 *)
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vector(26, n, my(x=5/8); gamma(n-1+x)\gamma(x) ) \\ G. C. Greubel, Nov 17 2019
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[floor(rising_factorial(5/8, n)) for n in (0..25)] # G. C. Greubel, Nov 17 2019
A020072
a(n) = floor( Gamma(n+3/8)/Gamma(3/8) ).
Original entry on oeis.org
1, 0, 0, 1, 4, 18, 97, 619, 4569, 38269, 358778, 3722325, 42341447, 523975411, 7008171124, 100742459918, 1548915321245, 25363488385398, 440690610696307, 8097689971544644, 156892743198677492, 3196689642673053918
Offset: 0
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[Floor(Gamma(n+3/8)/Gamma(3/8)): n in [0..25]]; // G. C. Greubel, Nov 17 2019
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Digits := 64:f := proc(n,x) trunc(GAMMA(n+x)/GAMMA(x)); end;
seq(floor(pochhammer(3/8,n)), n = 0..25); # G. C. Greubel, Nov 17 2019
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Floor[Pochhammer[3/8, Range[0, 25]]] (* G. C. Greubel, Nov 17 2019 *)
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vector(26, n, my(x=3/8); gamma(n-1+x)\gamma(x) ) \\ G. C. Greubel, Nov 17 2019
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[floor(rising_factorial(3/8, n)) for n in (0..25)] # G. C. Greubel, Nov 17 2019
A020028
Nearest integer to Gamma(n + 1/8)/Gamma(1/8).
Original entry on oeis.org
1, 0, 0, 0, 1, 4, 20, 121, 862, 7000, 63876, 646743, 7195013, 87239530, 1145018832, 16173391002, 244622538903, 3944538439806, 67550220781672, 1224347751667801, 23415650750646696, 471239971356764754
Offset: 0
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Digits := 64:f := proc(n,x) round(GAMMA(n+x)/GAMMA(x)); end;
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Table[Round[Gamma[n+1/8]/Gamma[1/8]],{n,0,30}] (* Harvey P. Dale, Sep 05 2020 *)
Showing 1-4 of 4 results.
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