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 A319873 a(n) = 9*8*7*6*5*4*3*2*1 + 18*17*16*15*14*13*12*11*10 + ... + (up to the n-th term). 9
 9, 72, 504, 3024, 15120, 60480, 181440, 362880, 362880, 362898, 363186, 367776, 436320, 1391040, 13728960, 160755840, 1764685440, 17643588480, 17643588507, 17643589182, 17643606030, 17644009680, 17653276080, 17856715680, 22119259680, 107157012480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For similar multiply/add sequences in descending blocks of k natural numbers, we have: a(n) = Sum_{j=1..k-1} (floor((n-j)/k)-floor((n-j-1)/k)) * (Product_{i=1..j} n-i-j+k+1) + Sum_{j=1..n} (floor(j/k)-floor((j-1)/k)) * (Product_{i=1..k} j-i+1). Here, k=9. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 EXAMPLE a(1) = 9; a(2) = 9*8 = 72; a(3) = 9*8*7 = 504; a(4) = 9*8*7*6 = 3024; a(5) = 9*8*7*6*5 = 15120; a(6) = 9*8*7*6*5*4 = 60480; a(7) = 9*8*7*6*5*4*3 = 181440; a(8) = 9*8*7*6*5*4*3*2 = 362880; a(9) = 9*8*7*6*5*4*3*2*1 = 362880; a(10) = 9*8*7*6*5*4*3*2*1 + 18 = 362898; a(11) = 9*8*7*6*5*4*3*2*1 + 18*17 = 363186; a(12) = 9*8*7*6*5*4*3*2*1 + 18*17*16 = 367776 a(13) = 9*8*7*6*5*4*3*2*1 + 18*17*16*15 = 436320; a(14) = 9*8*7*6*5*4*3*2*1 + 18*17*16*15*14 = 1391040; a(15) = 9*8*7*6*5*4*3*2*1 + 18*17*16*15*14*13 = 13728960; a(16) = 9*8*7*6*5*4*3*2*1 + 18*17*16*15*14*13*12 = 160755840; a(17) = 9*8*7*6*5*4*3*2*1 + 18*17*16*15*14*13*12*11 = 1764685440; a(18) = 9*8*7*6*5*4*3*2*1 + 18*17*16*15*14*13*12*11*10 = 17643588480; a(19) = 9*8*7*6*5*4*3*2*1 + 18*17*16*15*14*13*12*11*10 + 27 = 17643588507; etc. MAPLE a:=(n, k)->add((floor((n-j)/k)-floor((n-j-1)/k))*(mul(n-i-j+k+1, i=1..j)), j=1..k-1) + add((floor(j/k)-floor((j-1)/k))*(mul(j-i+1, i=1..k)), j=1..n): seq(a(n, 9), n=1..30); # Muniru A Asiru, Sep 30 2018 MATHEMATICA k:=9; a[n_]:=Sum[(Floor[(n-j)/k]-Floor[(n-j-1)/k])* Product[n-i-j+k+1, {i, 1, j }], {j, 1, k-1} ] + Sum[(Floor[j/k]-Floor[(j-1)/k])* Product[j-i+1, {i, 1, k} ], {j, 1, n}]; Array[a, 50] (* Stefano Spezia, Sep 30 2018 *) CROSSREFS For similar sequences, see: A000217 (k=1), A319866 (k=2), A319867 (k=3), A319868 (k=4), A319869 (k=5), A319870 (k=6), A319871 (k=7), A319872 (k=8), this sequence (k=9), A319874 (k=10). Sequence in context: A005778 A288351 A319892 * A110396 A162755 A045993 Adjacent sequences: A319870 A319871 A319872 * A319874 A319875 A319876 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Sep 30 2018 STATUS approved

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Last modified September 17 04:31 EDT 2024. Contains 375985 sequences. (Running on oeis4.)