A138523 a(n) = Sum_{k=1..n} (2k-1)!.

1, 7, 127, 5167, 368047, 40284847, 6267305647, 1313941673647, 357001369769647, 122002101778601647, 51212944273488041647, 25903229683158464681647, 15537113273014144448681647, 10904406563691366305216681647, 8852666400303393320848832681647, 8231691320578226211046411712681647

Offset: 1

Author

Leroy Quet, Mar 23 2008

Keywords

• easy
• nonn

Comments

a(n) is divisible by 107 for n >= 53. - Robert Israel, Dec 01 2015

Last digit is 7 for n > 1. Therefore there is no square in this sequence except 1. - Altug Alkan, Dec 01 2015

a(n) is the rank of [2,1, 4,3, ..., 2n,2n-1] within the permutations of [1, 2, ... 2n-1, 2n] in lexicographic order. See A375302 for the ranking function. - Hugo Pfoertner, Aug 25 2024

Links

• G. C. Greubel, Table of n, a(n) for n = 1..225

Crossrefs

Cf. A007489, A138524, A138525, A375302.

Programs

Maple

a:=proc(n) options operator, arrow: sum(factorial(2*k-1), k=1..n) end proc: seq(a(n), n=1..14); # Emeric Deutsch, Mar 31 2008

Mathematica

Table[Sum[(2i - 1)!, {i, n}], {n, 15}] (* Stefan Steinerberger, Mar 25 2008 *)

PARI

a(n) = sum(k=1, n, (2*k-1)!); \\ Michel Marcus, Oct 28 2015

Formula

Recurrence: a(1) = 1, a(2) = 7, a(n) = (4*n^2-6*n+3)*a(n-1) - 2*(n-1)*(2*n-1)*a(n-2). - Vladimir Reshetnikov, Oct 28 2015

Extensions

More terms from Stefan Steinerberger, Emeric Deutsch and Robert G. Wilson v, Mar 25 2008