A082430 a(1)=1; for n > 1, a(n) = n*(a(n-1) + a(n-2) + ... + a(2) + a(1)) + 4.

1, 6, 25, 132, 824, 5932, 48444, 442916, 4484524, 49828044, 602919332, 7892762164, 111156400476, 1675896499484, 26934050884564, 459674468429892, 8302870086014924, 158242935756990316, 3173649989348528004

Offset

1,2

Comments

More generally, if m is an integer and a(1)=1, a(n) = n*(a(n-1) + a(n-2) + ... + a(2) + a(1)) + m then a(n) has a closed form formula as a(n) = floor/ceiling(n*r(m)*n!) where r(m) = frac(e*m) + 0 or + 1/2 or -1/2 + integer. (See Example section.)

Links

Harvey P. Dale, Table of n, a(n) for n = 1..448

Formula

For n >= 2, a(n) = ceiling(n*(19/2 - 4*e)*n!).

Example

r(10) = frac(10*e) + 1/2 + 2;
r(12) = frac(12*e) - 1/2 + 3;
r(15) = frac(15*e) + 3;
r(18) = frac(18*e) - 1/2 + 4.

Mathematica

nxt[{n_, t_, a_}]:=Module[{c=t(n+1)+4}, {n+1, t+c, c}]; NestList[nxt, {1, 1, 1}, 20][[;; , 3]] (* Harvey P. Dale, Mar 28 2024 *)

Crossrefs

Cf. A007808, A074143.

Sequence in context: A073967 A188207 A275541 * A136593 A012293 A012594

Adjacent sequences: A082427 A082428 A082429 * A082431 A082432 A082433

Keyword

nonn

Author

Benoit Cloitre, Apr 24 2003

Status

approved