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A054091 Row sums of A054090. 9
1, 2, 4, 10, 32, 130, 652, 3914, 27400, 219202, 1972820, 19728202, 217010224, 2604122690, 33853594972, 473950329610, 7109254944152, 113748079106434, 1933717344809380, 34806912206568842, 661331331924808000, 13226626638496160002 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums of A094816 as a triangular array as follows: {1}, {1,1}, {1,3}, {1,1,8}, {6,1,1,24}, {29,10,1,1,89}, ... - Michael Somos, Nov 19 2006

a(n) = (n-1)a(n-1)+2, n>0; 2=0*1+2, 4=1*2+2, 10=2*4+2, ... - Gary Detlefs, May 20 2010

Row sums of triangle A208058. - Gary W. Adamson, Feb 22 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

FORMULA

a(n+1) = Sum(2*n!/j!, j=0..n). - Zerinvary Lajos, Oct 20 2006

a(n) = 2*floor(e*(n-1)!), n>1. - Gary Detlefs, May 20 2010

a(n) = n*a(n-1) - (n-2)*a(n-2), a(0)=1, a(1)=2. - Vincenzo Librandi, Feb 23 2012

MAPLE

a:= n-> `if`( n=0, 1, add(2*(n-1)!/j!, j=0..n-1)): seq(a(n), n=0..18); # Zerinvary Lajos, Oct 20 2006

PROG

(PARI) {a(n)= local(A); if(n<1, n==0, A=vector(n); A[1]=2; for(k=1, n-1, A[k+1]=k*A[k]+2); A[n])} /* Michael Somos, Nov 19 2006 */

(PARI) {a(n)= if(n<1, n==0, n--; n!*polcoeff( 2*exp(x+x*O(x^n))/(1-x), n))} /* Michael Somos, Nov 19 2006 */

CROSSREFS

a(n+1) = 2*A000522(n).

Cf. A208058.

Sequence in context: A009284 A105557 A166741 * A056593 A154219 A173489

Adjacent sequences:  A054088 A054089 A054090 * A054092 A054093 A054094

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified September 29 04:22 EDT 2020. Contains 337420 sequences. (Running on oeis4.)