A319893 a(n) = 10*9*8*7*6*5*4*3*2*1 - 20*19*18*17*16*15*14*13*12*11 + 30*19*18*17*16*15*14*13*12*11 - ... + (up to the n-th term).

10, 90, 720, 5040, 30240, 151200, 604800, 1814400, 3628800, 3628800, 3628780, 3628420, 3621960, 3512520, 1768320, -24278400, -387072000, -5075481600, -60945696000, -670438944000, -670438943970, -670438943130, -670438919640, -670438286280, -670421843280

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=10.

Links

Table of n, a(n) for n=1..25.

Example

a(1) = 10;
a(2) = 10*9 = 90;
a(3) = 10*9*8 = 720;
a(4) = 10*9*8*7 = 5040;
a(5) = 10*9*8*7*6 = 30240;
a(6) = 10*9*8*7*6*5 = 151200;
a(7) = 10*9*8*7*6*5*4 = 604800;
a(8) = 10*9*8*7*6*5*4*3 = 1814400;
a(9) = 10*9*8*7*6*5*4*3*2 = 3628800;
a(10) = 10*9*8*7*6*5*4*3*2*1 = 3628800;
a(11) = 10*9*8*7*6*5*4*3*2*1 - 20 = 3628780;
a(12) = 10*9*8*7*6*5*4*3*2*1 - 20*19 = 3628420;
a(13) = 10*9*8*7*6*5*4*3*2*1 - 20*19*18 = 3621960;
a(14) = 10*9*8*7*6*5*4*3*2*1 - 20*19*18*17 = 3512520;
a(15) = 10*9*8*7*6*5*4*3*2*1 - 20*19*18*17*16 = 1768320;
a(16) = 10*9*8*7*6*5*4*3*2*1 - 20*19*18*17*16*15 = -24278400;
a(17) = 10*9*8*7*6*5*4*3*2*1 - 20*19*18*17*16*15*14 = -387072000;
a(18) = 10*9*8*7*6*5*4*3*2*1 - 20*19*18*17*16*15*14*13 = -5075481600;
a(19) = 10*9*8*7*6*5*4*3*2*1 - 20*19*18*17*16*15*14*13*12 = -60945696000;
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, 10), 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), A319892 (k=9), this sequence (k=10).

Sequence in context: A228418 A306958 A306957 * A319874 A159733 A265325

Adjacent sequences: A319890 A319891 A319892 * A319894 A319895 A319896

Keyword

sign,easy

Author

Wesley Ivan Hurt, Sep 30 2018

Status

approved