A123636 a(n) = 1 + 1*n + 1*n*2 + 1*n*2*(n-1) + 1*n*2*(n-1)*3 + 1*n*2*(n-1)*3*(n-2) + ... + n!.

1, 1, 3, 10, 37, 176, 979, 6658, 50873, 451180, 4376911, 47740694, 560586613, 7248848608, 99837660875, 1492197903466, 23571796088689, 399706304138708, 7121101849585543, 135049981967575870, 2678257990821099821

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..449

Formula

a(n) = 1 + Sum_{k=1..n} (floor((k + 1)/2)! * n!)/((n - floor(k/2))!) ). - G. C. Greubel, Oct 26 2017

a(n) ~ n!. - Vaclav Kotesovec, Oct 09 2020

Example

a(0) = a(1) = 1;
a(2) = 1 + 1*2 = 3;
a(3) = 1 + 1*3 + 1*3*2 = 10;
a(4) = 1 + 1*4 + 1*4*2 + 1*4*2*3 = 37;
a(5) = 1 + 1*5 + 1*5*2 + 1*5*2*4 + 1*5*2*4*3 = 176; ...

Mathematica

Join[{1}, Table[Sum[(Floor[(k + 1)/2]! * n!)/((n - Floor[k/2])!), {k, 1, n}], {n, 1, 50}]] (* G. C. Greubel, Oct 26 2017 *)

Prog

(PARI) {a(n)=if(n==0, 1, sum(k=1, n, prod(j=1, k, ((j+1)\2)*(j%2)+(n+1-(j\2))*((j-1)%2))))}

Crossrefs

Cf. A123637.

Sequence in context: A363294 A289990 A370369 * A371901 A092816 A078109

Adjacent sequences: A123633 A123634 A123635 * A123637 A123638 A123639

Keyword

nonn

Author

Paul D. Hanna, Oct 03 2006

Status

approved