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A227037 Partial sums of A013999. 1
1, 2, 4, 12, 54, 312, 2136, 16800, 149160, 1475280, 16081920, 191530080, 2473999920, 34446303360, 514240110720, 8193624284160, 138780284791680, 2489891543596800, 47169750454848000, 940914453958617600, 19712190644360121600 (list; graph; refs; listen; history; text; internal format)
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: A058767 A075876 A222470 * A158569 A020106 A099928

Adjacent sequences:  A227034 A227035 A227036 * A227038 A227039 A227040

KEYWORD

nonn

AUTHOR

Emanuele Munarini, Jul 01 2013

STATUS

approved

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Last modified October 1 08:39 EDT 2020. Contains 337442 sequences. (Running on oeis4.)