A107713 Convolution of 2^n*n! and n!.

1, 3, 12, 66, 484, 4536, 52128, 709776, 11153376, 198339840, 3932962560, 85976743680, 2053285148160, 53173906652160, 1483987541299200, 44396218792396800, 1417294759310438400, 48088097391133900800, 1728013936221838540800, 65558270633421791232000

Offset

0,2

Comments

E.g.f. is int( 1/((1-t)(1-2*(x+t))), t=0..x).

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..n} 2^k * k! * (n-k)!.

E.g.f. (for offset 1): (log(1-x)+log(1-2*x))/(-3+2*x).

a(n) ~ n! * 2^n * (1 + 1/(2*n) + 1/(2*n^2) + 5/(4*n^3) + 17/(4*n^4) + 37/(2*n^5) + 98/n^6 + 4885/(8*n^7) + 34969/(8*n^8) + 70657/(2*n^9) + 636151/(2*n^10) + ...). - Vaclav Kotesovec, Aug 08 2019, extended Dec 07 2020

Example

a(4) = 484 = 4! 0! + 2 3! 1! + 2^2 2! 2! + 2^3 1! 3! + 2^4 0! 4!

Maple

f:=proc(n) local k; add(2^k*k!*(n-k)!, k=0..n); end:

Mathematica

Rest[Range[0, 20]! CoefficientList[Series[((Log[1 - x] + Log[1 - 2 x]))/(-3 + 2 x), {x, 0, 20}], x]] (* Vincenzo Librandi, Jul 13 2015 *)
Table[Sum[2^k * k! * (n-k)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 08 2019 *)

Crossrefs

Cf. A003149, A108953, A110467.

Sequence in context: A009362 A123227 A196556 * A375227 A289539 A370342

Adjacent sequences: A107710 A107711 A107712 * A107714 A107715 A107716

Keyword

nonn

Author

Mike Zabrocki, Jun 10 2005

Status

approved