Guess A Formula

Give a formula for the following sequence: 1 1 2 3 8 10 18 21 64 72 100 110 216 234 294 315 1024 1088 1296 1368 2000 2100 2420 2530 5184 5400 6084 6318 8232 8526 9450 9765 32768 33792 36992 38080 46656 47952 51984 53352 80000 82000 88200 90300 106480 108900 116380 118910 248832 254016 270000 275400 316368 322452 341172 347490 460992 469224 494508 503034 567000 576450 605430 615195 2097152 2129920 2230272 2264064 2515456 2552448 2665600 2703680 3359232 3405888 3548448 3596400 3950784 4002768 4161456 4214808 6400000 6480000 6724000 6806000 7408800 7497000 7765800 7856100 9370240 9476720 9801000 9909900 10706960 10823340 11177540 11296450 23887872 24136704 24893568 25147584...

L(x):=∑kj=0f(xj)ℓj(x) = 2×−(x−1368)1366×−(x−2000)1998×−(x−2100)2098×−(x−6084)6082×−(x−6318)6316×−(x−8232)8230×−(x−8526)8524×−(x−9450)9448×−(x−9765)9763 + 1368×x−21366×−(x−2000)632×−(x−2100)732×−(x−6084)4716×−(x−6318)4950×−(x−8232)6864×−(x−8526)7158×−(x−9450)8082×−(x−9765)8397 + 2000×x−21998×x−1368632×−(x−2100)100×−(x−6084)4084×−(x−6318)4318×−(x−8232)6232×−(x−8526)6526×−(x−9450)7450×−(x−9765)7765 + 2100×x−22098×x−1368732×x−2000100×−(x−6084)3984×−(x−6318)4218×−(x−8232)6132×−(x−8526)6426×−(x−9450)7350×−(x−9765)7665 + 6084×x−26082×x−13684716×x−20004084×x−21003984×−(x−6318)234×−(x−8232)2148×−(x−8526)2442×−(x−9450)3366×−(x−9765)3681 + 6318×x−26316×x−13684950×x−20004318×x−21004218×x−6084234×−(x−8232)1914×−(x−8526)2208×−(x−9450)3132×−(x−9765)3447 + 8232×x−28230×x−13686864×x−20006232×x−21006132×x−60842148×x−63181914×−(x−8526)294×−(x−9450)1218×−(x−9765)1533 + 8526×x−28524×x−13687158×x−20006526×x−21006426×x−60842442×x−63182208×x−8232294×−(x−9450)924×−(x−9765)1239 + 9450×x−29448×x−13688082×x−20007450×x−21007350×x−60843366×x−63183132×x−82321218×x−8526924×−(x−9765)315 + 9765×x−29763×x−13688397×x−20007765×x−21007665×x−60843681×x−63183447×x−82321533×x−85261239×x−9450315