A073013 a(n) = (1/2) * Sum_{k=1..n} (n+k)!/(k!)^2.

1, 6, 37, 255, 1991, 17598, 174924, 1937715, 23696029, 317105778, 4608337064, 72249308222, 1215116713110, 21816229444012, 416367513788760, 8415762294812355, 179556294350582865, 4032049130587198650, 95044828751874519840, 2346284236366567126410, 60527222877161072721930

Offset

1,2

Comments

a(n) is odd for n = 1,3 and if n is of the form 2^m or 2^m+1 (with m>= 2) (i.e., a(n) is odd if n=1,3,4,5,8,9,16,17,32,33,64,65,128,129,256,257...).

Links

Table of n, a(n) for n=1..21.

Mathematica

Table[(Sum[(n+k)!/(k!)^2, {k, n}])/2, {n, 20}] (* Harvey P. Dale, Jun 14 2022 *)

Prog

(PARI) a(n)=if(n<0, 0, sum(k=1, n, (n+k)!/(k!)^2)/2)

Crossrefs

Sequence in context: A271905 A351152 A355957 * A192238 A140712 A362094

Adjacent sequences: A073010 A073011 A073012 * A073014 A073015 A073016

Keyword

easy,nonn

Author

Benoit Cloitre, Aug 03 2002

Extensions

More terms from Wesley Ivan Hurt, Dec 26 2023

Status

approved