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A319869 a(n) = 5*4*3*2*1 + 10*9*8*7*6 + 15*14*13*12*11 + ... + (up to the n-th term). 9
5, 20, 60, 120, 120, 130, 210, 840, 5160, 30360, 30375, 30570, 33090, 63120, 390720, 390740, 391100, 397560, 507000, 2251200, 2251225, 2251800, 2265000, 2554800, 8626800, 8626830, 8627670, 8651160, 9284520, 25727520, 25727555, 25728710, 25766790, 26984160 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For similar multiply/add sequences in descending blocks of k natural numbers, we have: a(n) = 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} (floor(j/k)-floor((j-1)/k)) * (Product_{i=1..k} j-i+1). Here, k=5.

LINKS

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

EXAMPLE

a(1) = 5;

a(2) = 5*4 = 20;

a(3) = 5*4*3 = 60;

a(4) = 5*4*3*2 = 120;

a(5) = 5*4*3*2*1 = 120;

a(6) = 5*4*3*2*1 + 10 = 130;

a(7) = 5*4*3*2*1 + 10*9 = 210;

a(8) = 5*4*3*2*1 + 10*9*8 = 840;

a(9) = 5*4*3*2*1 + 10*9*8*7 = 5160;

a(10) = 5*4*3*2*1 + 10*9*8*7*6 = 30360;

a(11) = 5*4*3*2*1 + 10*9*8*7*6 + 15 = 30375;

a(12) = 5*4*3*2*1 + 10*9*8*7*6 + 15*14 = 30570;

a(13) = 5*4*3*2*1 + 10*9*8*7*6 + 15*14*13 = 33090;

a(14) = 5*4*3*2*1 + 10*9*8*7*6 + 15*14*13*12 = 63120;

a(15) = 5*4*3*2*1 + 10*9*8*7*6 + 15*14*13*12*11 = 390720;

a(16) = 5*4*3*2*1 + 10*9*8*7*6 + 15*14*13*12*11 + 20 = 390740;

a(17) = 5*4*3*2*1 + 10*9*8*7*6 + 15*14*13*12*11 + 20*19 = 391100;

a(18) = 5*4*3*2*1 + 10*9*8*7*6 + 15*14*13*12*11 + 20*19*18 = 397560;

a(19) = 5*4*3*2*1 + 10*9*8*7*6 + 15*14*13*12*11 + 20*19*18*17 = 507000;

a(20) = 5*4*3*2*1 + 10*9*8*7*6 + 15*14*13*12*11 + 20*19*18*17*16 = 2251200;

etc.

MAPLE

a:=(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((floor(j/k)-floor((j-1)/k))*(mul(j-i+1, i=1..k)), j=1..n): seq(a(n, 5), n=1..40); # Muniru A Asiru, Sep 30 2018

MATHEMATICA

k:=5; a[n_]:=Sum[(Floor[(n-j)/k]-Floor[(n-j-1)/k])*Product[n-i-j+k+1, {i, 1, j }] , {j, 1, k-1}] + Sum[(Floor[j/k]-Floor[(j-1)/k])*Product[j-i+1, {i, 1, k}], {j, 1, n}]; Array[a, 50] (* Stefano Spezia, Sep 30 2018 *)

CROSSREFS

For similar sequences, see: A000217 (k=1), A319866 (k=2), A319867 (k=3), A319868 (k=4), this sequence (k=5), A319870 (k=6), A319871 (k=7), A319872 (k=8), A319873 (k=9), A319874 (k=10).

Sequence in context: A272507 A256540 A319888 * A038165 A327383 A215224

Adjacent sequences:  A319866 A319867 A319868 * A319870 A319871 A319872

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Sep 29 2018

STATUS

approved

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Last modified November 13 04:20 EST 2019. Contains 329085 sequences. (Running on oeis4.)