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 A319550 a(n) = 1*2*3*4*5*6*7*8*9 - 10*11*12*13*14*15*16*17*18 + 19*20*21*22*23*24*25*26*27 - ... + (up to n). 8
 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 362870, 362770, 361560, 345720, 122640, -3240720, -57294720, -979816320, -17642862720, -17642862701, -17642862340, -17642854740, -17642687160, -17638824840, -17545953600, -15220134720, 45348065280, 1683112193280 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In general, for alternating sequences that multiply the first k natural numbers, and subtract/add the products of the next k natural numbers (preserving the order of operations up to n), we have a(n) = (-1)^floor(n/k) * Sum_{i=1..k-1} (1-sign((n-i) mod k)) * (Product_{j=1..i} (n-j+1)) + Sum_{i=1..n} (-1)^(floor(i/k)+1) * (1-sign(i mod k)) * (Product_{j=1..k} (i-j+1)). Here k=9. An alternating version of A319211. LINKS FORMULA a(n) = (-1)^floor(n/9) * Sum_{i=1..8} (1-sign((n-i) mod 9)) * (Product_{j=1..i} (n-j+1)) + Sum_{i=1..n} (-1)^(floor(i/9)+1) * (1-sign(i mod 9)) * (Product_{j=1..9} (i-j+1)). EXAMPLE a(1) = 1; a(2) = 1*2 = 2; a(3) = 1*2*3 = 6; a(4) = 1*2*3*4 = 24; a(5) = 1*2*3*4*5 = 120; a(6) = 1*2*3*4*5*6 = 720; a(7) = 1*2*3*4*5*6*7 = 5040; a(8) = 1*2*3*4*5*6*7*8 = 40320; a(9) = 1*2*3*4*5*6*7*8*9 = 362880; a(10) = 1*2*3*4*5*6*7*8*9 - 10 = 362870; a(11) = 1*2*3*4*5*6*7*8*9 - 10*11 = 362770; a(12) = 1*2*3*4*5*6*7*8*9 - 10*11*12 = 361560; a(13) = 1*2*3*4*5*6*7*8*9 - 10*11*12*13 = 345720; a(14) = 1*2*3*4*5*6*7*8*9 - 10*11*12*13*14 = 122640; a(15) = 1*2*3*4*5*6*7*8*9 - 10*11*12*13*14*15 = -3240720; a(16) = 1*2*3*4*5*6*7*8*9 - 10*11*12*13*14*15*16 = -57294720; a(17) = 1*2*3*4*5*6*7*8*9 - 10*11*12*13*14*15*16*17 = -979816320; a(18) = 1*2*3*4*5*6*7*8*9 - 10*11*12*13*14*15*16*17*18 = -17642862720; a(19) = 1*2*3*4*5*6*7*8*9 - 10*11*12*13*14*15*16*17*18 + 19 = -17642862701; etc. CROSSREFS For similar sequences, see: A001057 (k=1), A319373 (k=2), A319543 (k=3), A319544 (k=4), A319545 (k=5), A319546 (k=6), A319547 (k=7), A319549 (k=8), this sequence (k=9), A319551 (k=10). Cf. A319211. Sequence in context: A182287 A248778 A033647 * A109834 A131451 A084012 Adjacent sequences:  A319547 A319548 A319549 * A319551 A319552 A319553 KEYWORD sign,easy AUTHOR Wesley Ivan Hurt, Sep 22 2018 STATUS approved

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Last modified June 12 16:05 EDT 2021. Contains 344959 sequences. (Running on oeis4.)