n_list Exact solution Stirling Absolute error Relative error 10 15.1044 13.0259 2.0786 0.1376 12 19.9872 17.8189 2.1683 0.1085 15 27.8993 25.6208 2.2785 0.0817 20 42.3356 39.9146 2.4210 0.0572 25 58.0036 55.4719 2.5317 0.0436 32 81.5580 78.9035 2.6544 0.0325 40 110.3206 107.5552 2.7655 0.0251 51 152.4096 149.5231 2.8865 0.0189 65 209.3426 206.3352 3.0074 0.0144 82 282.4743 279.3510 3.1233 0.0111 104 382.2586 379.0167 3.2419 0.0085 132 515.8908 512.5299 3.3610 0.0065 167 691.1834 687.7050 3.4784 0.0050 212 927.1939 923.5963 3.5976 0.0039 268 1234.0993 1230.3845 3.7147 0.0030 339 1639.8462 1636.0140 3.8322 0.0023 429 2175.3149 2171.3650 3.9499 0.0018 542 2874.1009 2870.0342 4.0667 0.0014 686 3798.3666 3794.1821 4.1845 0.0011 868 5009.3565 5005.0544 4.3021 0.0009 1098 6593.7873 6589.3677 4.4196 0.0007 1389 8666.8125 8662.2753 4.5372 0.0005 1757 11374.8396 11370.1849 4.6547 0.0004 2222 14905.8662 14901.0941 4.7721 0.0003 2811 19516.8715 19511.9818 4.8896 0.0003 3556 25524.2557 25519.2485 5.0072 0.0002 4498 33341.5485 33336.4238 5.1247 0.0002 5689 43504.9846 43499.7425 5.2421 0.0001 7196 56719.0548 56713.6952 5.3596 0.0001 9102 73879.5796 73874.1025 5.4771 0.0001 11513 96153.3299 96147.7353 5.5946 0.0001 14563 125047.1156 125041.4036 5.7121 0.0000 18420 162492.1919 162486.3623 5.8295 0.0000 23299 211005.5521 210999.6051 5.9470 0.0000 29470 273815.6089 273809.5444 6.0645 0.0000 37275 355090.7446 355084.5627 6.1820 0.0000 47148 460220.1373 460213.8378 6.2995 0.0000 59636 596128.7495 596122.3325 6.4169 0.0000 75431 771739.1048 771732.5704 6.5344 0.0000 95409 998550.3948 998543.7429 6.6519 0.0000 120679 1291379.4021 1291372.6327 6.7694 0.0000 152641 1669265.0567 1669258.1698 6.8869 0.0000 193069 2156742.7527 2156735.7484 7.0043 0.0000 244205 2785351.5523 2785344.4305 7.1218 0.0000 308884 3595639.7296 3595632.4903 7.2393 0.0000 390693 4639751.3733 4639744.0165 7.3568 0.0000 494171 5984733.0169 5984725.5426 7.4743 0.0000 625055 7716683.4275 7716675.8358 7.5917 0.0000 790604 9946242.8294 9946235.1202 7.7092 0.0000 1000000 12815518.3847 12815510.5580 7.8267 0.0000