A227037 Partial sums of A013999.

1, 2, 4, 12, 54, 312, 2136, 16800, 149160, 1475280, 16081920, 191530080, 2473999920, 34446303360, 514240110720, 8193624284160, 138780284791680, 2489891543596800, 47169750454848000, 940914453958617600, 19712190644360121600

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = sum(A013999(k), k=0..n).

a(n) = sum(sum(C(j-k+1,k)*(-1)^k*(j-k+1)!, k=0..floor((j+1)/2)), j=0..n).

Recurrence: a(n+4) -(n+8)*a(n+3) +(3*n+16)*a(n+2) -(3*n+13)*a(n+1) +(n+4)*a(n) = 0.

G.f.: Sum_{k>=0} (k+1)!*(x-x^2)^k.

a(n) = (n+3)*a(n-1)-2*(n+1)*a(n-2)+(n+1)*a(n-3) for n>2, a(n) = 2^n for n<=2. - Alois P. Heinz, Jul 01 2013

a(n) ~ n!*n/exp(1). - Vaclav Kotesovec, Jul 06 2013

Maple

a:= proc(n) option remember; `if`(n<3, 2^n,
      (n+3)*a(n-1) -2*(n+1)*a(n-2) +(n+1)*a(n-3))
    end:
seq(a(n), n=0..30);  # Alois P. Heinz, Jul 01 2013

Mathematica

Table[Sum[Sum[Binomial[j-k+1, k]*(-1)^k*(j-k+1)!, {k, 0, Floor[(j+1)/2]}], {j, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 06 2013 *)

Prog

(Maxima) makelist(sum(sum(binomial(j-k+1, k)*(-1)^k*(j-k+1)!, k, 0, floor((j+1)/2)), j, 0, n), n, 0, 20);

Crossrefs

Cf. A013999.

Sequence in context: A075876 A222470 A372347 * A158569 A020106 A099928

Adjacent sequences: A227034 A227035 A227036 * A227038 A227039 A227040

Keyword

nonn

Author

Emanuele Munarini, Jul 01 2013

Status

approved