A154028 a(2n) = n*(n+1)/2, a(2n+1) = n!.

0, 1, 1, 1, 3, 2, 6, 6, 10, 24, 15, 120, 21, 720, 28, 5040, 36, 40320, 45, 362880, 55, 3628800, 66, 39916800, 78, 479001600, 91, 6227020800, 105, 87178291200, 120, 1307674368000, 136, 20922789888000, 153, 355687428096000, 171

Offset

0,5

Comments

a(n) = n + a(n-1), a(n) = n*(n+1)/2, with a(0) = 0 and b(n) = n*a(n-1), a(n) = n!, with b(0) = 1, then you can form a function F such that: F(n!) = n*(n+1)/2.

Links

G. C. Greubel, Table of n, a(n) for n = 0..900

Mathematica

Flatten[Table[{n*(n + 1)/2, n!}, {n, 0, 20}]] (* Produces terms *)
(*addition*)
a[0] = 0; a[n_] := a[n] = n + a[n - 1];
Table[a[n] - n*(n + 1)/2, {n, 0, 20}] (* Demonstrates that a[n] = n*(n+1)/2 *)
(*multiplication*)
b[0] = 1; b[n_] := b[n] = n*b[n - 1];
Table[b[n] - n!, {n, 0, 20}] (* Demonstrates that b[n] = n! *)

Prog

(PARI) a(n)=if(n%2, (n\2)!, n*(n+2)/8) \\ Charles R Greathouse IV, Sep 01 2016

Crossrefs

Sequence in context: A286970 A347743 A023360 * A157793 A096375 A062200

Adjacent sequences: A154025 A154026 A154027 * A154029 A154030 A154031

Keyword

nonn,easy

Author

Roger L. Bagula, Jan 04 2009

Status

approved