A319891 a(n) = 8*7*6*5*4*3*2*1 - 16*15*14*13*12*11*10*9 + 24*23*22*21*20*19*18*17 - ... + (up to the n-th term).

8, 56, 336, 1680, 6720, 20160, 40320, 40320, 40304, 40080, 36960, -3360, -483840, -5725440, -57617280, -518878080, -518878056, -518877528, -518865936, -518623056, -513777600, -421968960, 1225486080, 29135312640, 29135312608, 29135311648, 29135282880

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=8.

Links

Table of n, a(n) for n=1..27.

Example

a(1) = 8;
a(2) = 8*7 = 56;
a(3) = 8*7*6 = 336;
a(4) = 8*7*6*5 = 1680;
a(5) = 8*7*6*5*4 = 6720;
a(6) = 8*7*6*5*4*3 = 20160;
a(7) = 8*7*6*5*4*3*2 = 40320;
a(8) = 8*7*6*5*4*3*2*1 = 40320;
a(9) = 8*7*6*5*4*3*2*1 - 16 = 40304;
a(10) = 8*7*6*5*4*3*2*1 - 16*15 = 40080;
a(11) = 8*7*6*5*4*3*2*1 - 16*15*14 = 36960;
a(12) = 8*7*6*5*4*3*2*1 - 16*15*14*13 = -3360;
a(13) = 8*7*6*5*4*3*2*1 - 16*15*14*13*12 = -483840;
a(14) = 8*7*6*5*4*3*2*1 - 16*15*14*13*12*11 = -5725440;
a(15) = 8*7*6*5*4*3*2*1 - 16*15*14*13*12*11*10 = -57617280;
a(16) = 8*7*6*5*4*3*2*1 - 16*15*14*13*12*11*10*9 = -518878080;
a(17) = 8*7*6*5*4*3*2*1 - 16*15*14*13*12*11*10*9 + 24 = -518878056;
a(18) = 8*7*6*5*4*3*2*1 - 16*15*14*13*12*11*10*9 + 24*23 = -518877528;
a(19) = 8*7*6*5*4*3*2*1 - 16*15*14*13*12*11*10*9 + 24*23*22 = -518865936;
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, 8), 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), this sequence (k=8), A319892 (k=9), A319893 (k=10).

Sequence in context: A334332 A068552 A264946 * A319872 A215227 A034006

Adjacent sequences: A319888 A319889 A319890 * A319892 A319893 A319894

Keyword

sign,easy

Author

Wesley Ivan Hurt, Sep 30 2018

Status

approved