cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A138524 a(n) = Sum_{k=1..n} (2*k)!.

Original entry on oeis.org

2, 26, 746, 41066, 3669866, 482671466, 87660962666, 21010450850666, 6423384156578666, 2439325392333218666, 1126440053169940898666, 621574841786409380258666, 403913035968392044964258666, 305292257647682252546468258666
Offset: 1

Views

Author

Leroy Quet, Mar 23 2008

Keywords

Crossrefs

Programs

  • Mathematica
    Table[Sum[(2*i)!, {i,n}], {n,15}] (* Stefan Steinerberger, Mar 25 2008 *)
    Accumulate[(2*Range[20])!] (* Harvey P. Dale, Nov 12 2016 *)
  • PARI
    for(n=1,25, print1(sum(k=1,n, (2*k)!), ", ")) \\ G. C. Greubel, Sep 29 2017
    
  • Python
    from math import factorial
    def a(n): return sum(factorial(2*k) for k in range(1, n+1))
    print([a(n) for n in range(1, 16)]) # Michael S. Branicky, Feb 26 2021

Formula

A007623(a(n)) = A163662(n). - Amiram Eldar, Apr 07 2022

Extensions

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

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

Original entry on oeis.org

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

Views

Author

Leroy Quet, Mar 23 2008

Keywords

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

Crossrefs

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

A290044 a(n) = |Sum_{k=0..n} (-1)^k*(2k)!!|.

Original entry on oeis.org

1, 1, 7, 41, 343, 3497, 42583, 602537, 9719383, 176075177, 3539816023, 78209790377, 1883780763223, 49127973630377, 1379201149390423, 41470672541233577, 329725285558734423, 45290937289840177577, 1633052915424520654423, 62144013487721190961577
Offset: 0

Views

Author

XU Pingya, Jul 19 2017

Keywords

Comments

a(20) = 19 * 47 * 73 * 54470291 * 700938921577. Thus a(n) are multiples of 19 for n >= 20.

Crossrefs

Programs

  • Mathematica
    Table[Abs@ Sum[(-1)^k*(2 k)!!, {k, 0, n}], {n, 0, 19}] (* Michael De Vlieger, Jul 19 2017 *)

A290046 a(n) = |Sum_{k=0..n} (-1)^k*(3k)!!|.

Original entry on oeis.org

1, 2, 46, 899, 45181, 1981844, 183812716, 13565497859, 1948425055741, 11509621621134, 42638364069002866, 6290021506693847759, 1672053831207666984241, 318158932941670103831384, 106827312624343125411048616, 25266964023001914822246560759
Offset: 0

Views

Author

XU Pingya, Jul 19 2017

Keywords

Comments

a(26) = 2 * 41 * 121157 * 160215276888781 * 1706504288791033 * 4123576055576581869533. Thus a(n) are multiples of 41 for n >= 26.

Crossrefs

Programs

  • Mathematica
    Table[Abs@ Sum[(-1)^k*(3 k)!!, {k, 0, n}], {n, 0, 15}] (* Michael De Vlieger, Jul 19 2017 *)
Showing 1-4 of 4 results.