A014510 -id:A014510 - cp's OEIS frontend

A014511 a(n) = floor( Gamma(n+1/3) ).

2, 0, 1, 2, 9, 40, 214, 1355, 9940, 82834, 773118, 7988887, 90540729, 1116669003, 14888920041, 213407853922, 3272253760146, 53446811415729, 926411397872639, 16984208960998389, 328361373245968867

Offset: 0

Simon Plouffe

nonn

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Amiram Eldar, Table of n, a(n) for n = 0..450
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Cf. A014510, A014512, A014513, A014514, A014516, A014517, A014518, A014521, A014522.

seq(floor(evalf(GAMMA(n+1/3),100)), n=0..24);

a[n_] := Floor[Gamma[n + 1/3]]; Array[a, 21, 0] (* Amiram Eldar, Sep 20 2019 *)

A014513 a(n) = floor( Gamma(n+1/4) ).

Original entry on oeis.org

3, 0, 1, 2, 8, 35, 184, 1155, 8376, 69106, 639232, 6552134, 73711509, 902965985, 11964299312, 170491265198, 2599991794272, 42249866656927, 728810199831991, 13300786146933842, 256040133328476465

Offset: 0

Simon Plouffe

nonn

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Amiram Eldar, Table of n, a(n) for n = 0..450
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Cf. A014510, A014511, A014512, A014514, A014516, A014517, A014518, A014521, A014522.

seq(floor(evalf(GAMMA(n+1/4),100)), n=0..24);

a[n_] := Floor[Gamma[n + 1/4]]; Array[a, 21, 0] (* Amiram Eldar, Sep 20 2019 *)

A014512 a(n) = floor( Gamma(n+2/3) ).

Original entry on oeis.org

1, 0, 1, 4, 14, 68, 389, 2593, 19884, 172328, 1665837, 17768938, 207304278, 2625854188, 35886673906, 526337883959, 8245960182038, 137432669700633, 2427977164711192, 45322240407942257, 891337394689531069

Offset: 0

Simon Plouffe

nonn

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Amiram Eldar, Table of n, a(n) for n = 0..450
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Cf. A014510, A014511, A014513, A014514, A014516, A014517, A014518, A014521, A014522.

seq(floor(evalf(GAMMA(n+2/3),100)), n=0..24);

a[n_] := Floor[Gamma[n + 2/3]]; Array[a, 21, 0] (* Amiram Eldar, Sep 20 2019 *)

A014514 a(n) = floor( Gamma(n+3/4) ).

Original entry on oeis.org

1, 0, 1, 4, 16, 78, 453, 3057, 23698, 207358, 2021746, 21733773, 255371835, 3255990905, 44769874946, 660355655453, 10400601573396, 174210076354396, 3092228855290534, 57979291036697518, 1145090997974775999, 23760638207976601980, 516793881023491093069

Offset: 0

Simon Plouffe

nonn

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Amiram Eldar, Table of n, a(n) for n = 0..450
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Cf. A014510, A014511, A014512, A014513, A014516, A014517, A014518, A014521, A014522.

[Floor(Gamma(n + 3/4)): n in [0..25]]; // Vincenzo Librandi, Aug 01 2025

seq(floor(evalf(GAMMA(n+3/4),100)), n=0..24);

a[n_] := Floor[Gamma[n + 3/4]]; Array[a, 21, 0] (* Amiram Eldar, Sep 20 2019 *)

A014516 Nearest integer to Gamma(n + 1/3).

Original entry on oeis.org

3, 1, 1, 3, 9, 40, 214, 1355, 9940, 82834, 773118, 7988888, 90540730, 1116669003, 14888920041, 213407853923, 3272253760147, 53446811415729, 926411397872639, 16984208960998390, 328361373245968868, 6676681256001366975, 142435866794695828799, 3181067691748206843170, 74224912807458159673978

Offset: 0

N. J. A. Sloane

nonn

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Robert Israel, Table of n, a(n) for n = 0..450
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Cf. A014510, A014511, A014512, A014513, A014514, A014517, A014518, A014521, A014522.

[ seq(round(evalf(GAMMA(n+1/3),100)), n=0..24) ];

a[n_] := Round[Gamma[n + 1/3]]; Array[a, 25, 0] (* Amiram Eldar, Sep 20 2019 *)

a(n) = round(gamma(n+1/3)); \\ Michel Marcus, Sep 13 2018

Corrected and extended by Robert Israel, Sep 12 2018

A014517 Nearest integer to Gamma(n+2/3).

Original entry on oeis.org

1, 1, 2, 4, 15, 69, 389, 2594, 19884, 172328, 1665838, 17768938, 207304278, 2625854188, 35886673906, 526337883960, 8245960182038, 137432669700634, 2427977164711192, 45322240407942258, 891337394689531069

Offset: 0

N. J. A. Sloane

nonn

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Amiram Eldar, Table of n, a(n) for n = 0..450
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Cf. A014510, A014511, A014512, A014513, A014514, A014516, A014518, A014521, A014522.

[ seq(round(evalf(GAMMA(n+2/3),100)), n=0..24) ];

a[n_] := Round[Gamma[n + 2/3]]; Array[a, 21, 0] (* Amiram Eldar, Sep 20 2019 *)

a(n) = round(gamma(n + 2/3)); \\ Michel Marcus, Nov 05 2018

a(15), a(17), and a(19) corrected by Sean A. Irvine, Nov 04 2018

A014518 Nearest integer to Gamma(n+1/4).

Original entry on oeis.org

4, 1, 1, 3, 8, 35, 185, 1155, 8377, 69106, 639233, 6552134, 73711509, 902965986, 11964299312, 170491265198, 2599991794272, 42249866656927, 728810199831991, 13300786146933842, 256040133328476466

Offset: 0

N. J. A. Sloane

nonn

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Amiram Eldar, Table of n, a(n) for n = 0..450
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Cf. A014510, A014511, A014512, A014513, A014514, A014516, A014517, A014521, A014522.

[ seq(round(evalf(GAMMA(n+1/4),100)), n=0..24) ];

a[n_] := Round[Gamma[n + 1/4]]; Array[a, 21, 0] (* Amiram Eldar, Sep 20 2019 *)

a(n) = round(gamma(n + 1/4)); \\ Michel Marcus, Nov 05 2018

a(20) corrected by Sean A. Irvine, Nov 04 2018

A014521 Nearest integer to Gamma(n+1/2).

Original entry on oeis.org

2, 1, 1, 3, 12, 52, 288, 1871, 14034, 119292, 1133278, 11899423, 136843365, 1710542068, 23092317922, 334838609874, 5189998453040, 85634974475162, 1498612053315336, 27724322986333718, 540624298233507504

Offset: 0

N. J. A. Sloane

nonn

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Amiram Eldar, Table of n, a(n) for n = 0..450
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Cf. A014510, A014511, A014512, A014513, A014514, A014516, A014517, A014518, A014522.

[ seq(round(evalf(GAMMA(n+1/2),100)), n=0..24) ];

Table[Round[Gamma[n + 1/2]], {n, 0, 26}]

a(n) = round(gamma(n + 1/2)); \\ Michel Marcus, Nov 05 2018

a(15) corrected by Sean A. Irvine, Nov 04 2018

A014522 Nearest integer to Gamma(n+3/4).

Original entry on oeis.org

1, 1, 2, 4, 17, 79, 453, 3058, 23698, 207359, 2021746, 21733773, 255371836, 3255990905, 44769874946, 660355655454, 10400601573397, 174210076354396, 3092228855290534, 57979291036697519, 1145090997974775999, 23760638207976601980, 516793881023491093070

Offset: 0

N. J. A. Sloane

nonn

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Amiram Eldar, Table of n, a(n) for n = 0..450
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 255.

Cf. A014510, A014511, A014512, A014513, A014514, A014516, A014517, A014518, A014521.

[ seq(round(evalf(GAMMA(n+3/4),100)), n=0..24) ];

a[n_] := Round[Gamma[n + 3/4]]; Array[a, 23, 0] (* Amiram Eldar, Sep 20 2019 *)

a(n) = round(gamma(n+3/4)) \\ Felix Fröhlich, Nov 05 2018

a(15), a(16), and a(19) corrected by Sean A. Irvine, Nov 05 2018

A284994 Floor(Gamma(n/2)).

Original entry on oeis.org

1, 1, 0, 1, 1, 2, 3, 6, 11, 24, 52, 120, 287, 720, 1871, 5040, 14034, 40320, 119292, 362880, 1133278, 3628800, 11899423, 39916800, 136843365, 479001600, 1710542068, 6227020800, 23092317922, 87178291200, 334838609873, 1307674368000, 5189998453040

Offset: 1

Clark Kimberling, Apr 08 2017

The bisections are A000142 (factorials) and A014510.

			Let s = sqrt(Pi); for n>=1, gamma(n/2) takes the values s, 1, s/2, 1, 3s/4, 2, 15s/8, 6, so that a(n) begins with 1,1,0,1,1,2,3,6.

Clark Kimberling, Table of n, a(n) for n = 1..500

Cf. A000142, A014510, A284995.

Mathematica
```
Table[Floor[Gamma[n/2]], {n, 1, 35}]
```

a(n) = floor(Gamma(n/2)).

cp's OEIS Frontend

A014511 a(n) = floor( Gamma(n+1/3) ).

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A014513 a(n) = floor( Gamma(n+1/4) ).

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A014512 a(n) = floor( Gamma(n+2/3) ).

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A014514 a(n) = floor( Gamma(n+3/4) ).

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Magma

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A014516 Nearest integer to Gamma(n + 1/3).

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A014517 Nearest integer to Gamma(n+2/3).

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A014518 Nearest integer to Gamma(n+1/4).

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A014521 Nearest integer to Gamma(n+1/2).

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