login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A347497 Alternating antidiagonal sums of A047920. 1
1, 1, 2, 5, 21, 105, 636, 4507, 36449, 330947, 3334302, 36913401, 445422501, 5818511965, 81805201736, 1231687676375, 19772907413361, 337146208373847, 6085000404767514, 115897246212304837, 2323089762369102677, 48883749655553977121, 1077440067884422805556 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..450

FORMULA

a(n) = Sum_{k=0..floor(n/2)} (-1)^k * A047920(n-k,k).

a(n) mod 2 = A152822(n).

MAPLE

b:= proc(n, k) option remember;

`if`(k=0, n!, b(n, k-1)-b(n-1, k-1))

end:

a:= n-> add(b(n-k, k)*(-1)^k, k=0..n/2):

seq(a(n), n=0..23);

MATHEMATICA

b[n_, k_] := b[n, k] = If[k == 0, n!, b[n, k-1] - b[n-1, k-1]];

a[n_] := Sum[b[n-k, k]*(-1)^k, {k, 0, n/2}];

Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Jun 05 2022, after Alois P. Heinz *)

CROSSREFS

Cf. A047920, A347429, A347431.

Sequence in context: A008981 A008982 A185134 * A130471 A002628 A357919

Adjacent sequences: A347494 A347495 A347496 * A347498 A347499 A347500

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 03 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 30 02:40 EST 2023. Contains 359939 sequences. (Running on oeis4.)