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A319209 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 + ... + (up to n). 10
1, 2, 6, 24, 120, 720, 5040, 40320, 40329, 40410, 41310, 52200, 194760, 2202480, 32472720, 518958720, 518958737, 518959026, 518964534, 519075000, 521400600, 572680080, 1754550000, 30173149440, 30173149465, 30173150090, 30173166990, 30173640840, 30187400040 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In general, for sequences that multiply the first k natural numbers, and then add the product of the next k natural numbers (preserving the order of operations up to n), we have a(n) = Sum_{i=1..floor(n/k)} (k*i)!/(k*i-k)! + Sum_{j=1..k-1} (1-sign((n-j) mod k)) * (Product_{i=1..j} n-i+1). Here, k=8.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Sum_{i=1..floor(n/8)} (8*i)!/(8*i-8)! + Sum_{j=1..7} (1-sign((n-j) mod 8)) * (Product_{i=1..j} n-i+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 = 40329;

a(10) = 1*2*3*4*5*6*7*8 + 9*10 = 40410;

a(11) = 1*2*3*4*5*6*7*8 + 9*10*11 = 41310;

a(12) = 1*2*3*4*5*6*7*8 + 9*10*11*12 = 52200;

a(13) = 1*2*3*4*5*6*7*8 + 9*10*11*12*13 = 194760;

a(14) = 1*2*3*4*5*6*7*8 + 9*10*11*12*13*14 = 2202480;

a(15) = 1*2*3*4*5*6*7*8 + 9*10*11*12*13*14*15 = 32472720;

a(16) = 1*2*3*4*5*6*7*8 + 9*10*11*12*13*14*15*16 = 518958720;

a(17) = 1*2*3*4*5*6*7*8 + 9*10*11*12*13*14*15*16 + 17 = 518958737;

a(18) = 1*2*3*4*5*6*7*8 + 9*10*11*12*13*14*15*16 + 17*18 = 518959026; etc.

CROSSREFS

Cf. A093361, (k=1) A000217, (k=2) A228958, (k=3) A319014, (k=4) A319205, (k=5) A319206, (k=6) A319207, (k=7) A319208, (k=8) this sequence, (k=9) A319211, (k=10) A319212.

Sequence in context: A067455 A033646 A319549 * A212310 A276842 A273695

Adjacent sequences:  A319206 A319207 A319208 * A319210 A319211 A319212

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Sep 13 2018

STATUS

approved

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Last modified July 13 13:27 EDT 2020. Contains 335688 sequences. (Running on oeis4.)