A319892 a(n) = 9*8*7*6*5*4*3*2*1 - 18*17*16*15*14*13*12*11*10 + 27*26*25*24*23*22*21*20*19 - ... + (up to the n-th term).

9, 72, 504, 3024, 15120, 60480, 181440, 362880, 362880, 362862, 362574, 357984, 289440, -665280, -13003200, -160030080, -1763959680, -17642862720, -17642862693, -17642862018, -17642845170, -17642441520, -17633175120, -17429735520, -13167191520, 71870561280

Offset

1,1

Comments

For similar sequences that alternate in descending blocks of k natural numbers, we have: a(n) = (-1)^floor(n/k) * 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} (-1)^(floor(j/k)+1) * (floor(j/k) - floor((j-1)/k)) * (Product_{i=1..k} j-i+1). Here, k=9.

Links

Table of n, a(n) for n=1..26.

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 = 362862;
a(11) = 9*8*7*6*5*4*3*2*1 - 18*17 = 362574;
a(12) = 9*8*7*6*5*4*3*2*1 - 18*17*16 = 357984;
a(13) = 9*8*7*6*5*4*3*2*1 - 18*17*16*15 = 289440;
a(14) = 9*8*7*6*5*4*3*2*1 - 18*17*16*15*14 = -665280;
a(15) = 9*8*7*6*5*4*3*2*1 - 18*17*16*15*14*13 = -13003200;
a(16) = 9*8*7*6*5*4*3*2*1 - 18*17*16*15*14*13*12 = -160030080;
a(17) = 9*8*7*6*5*4*3*2*1 - 18*17*16*15*14*13*12*11 = -1763959680;
a(18) = 9*8*7*6*5*4*3*2*1 - 18*17*16*15*14*13*12*11*10 = -17642862720;
a(19) = 9*8*7*6*5*4*3*2*1 - 18*17*16*15*14*13*12*11*10 + 27 = -17642862693;
etc.

Maple

a:=(n, k)->(-1)^(floor(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( (-1)^(floor(j/k)+1)*(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

Crossrefs

For similar sequences, see: A001057 (k=1), A319885 (k=2), A319886 (k=3), A319887 (k=4), A319888 (k=5), A319889 (k=6), A319890 (k=7), A319891 (k=8), this sequence (k=9), A319893 (k=10).

Sequence in context: A073988 A005778 A288351 * A319873 A110396 A162755

Adjacent sequences: A319889 A319890 A319891 * A319893 A319894 A319895

Keyword

sign,easy

Author

Wesley Ivan Hurt, Sep 30 2018

Status

approved