A259688 Related to Euler numbers.

1, 2, 8, 16, 136, 272, 3968, 7936, 176896, 353792, 11184128, 22368256, 951878656, 1903757312, 104932671488, 209865342976, 14544442556416, 29088885112832, 2475749026562048, 4951498053124096, 507711943253426176, 1015423886506852352, 123460740095103991808

Offset

0,2

Links

Table of n, a(n) for n=0..22.

C. Krishnamachary and M. Bheemasena Rao, Determinants whose elements are Eulerian, prepared Bernoullian and other numbers, J. Indian Math. Soc., 14 (1922), 55-62, 122-138 and 143-146. See p. 146. [Annotated scanned copy]

Formula

a(2n+1) = b(2n+3) for n >= 0, a(2n) = b(2n+3)/2 for n >= 0 where b(n) = A000111(n). - Mikhail Kurkov, Jun 13 2023 [verification needed]

Maple

b:= proc(u, o) option remember;
      `if`(u+o=0, 1, add(b(o-1+j, u-j), j=1..u))
    end:
a:= n-> `if`(n::odd, b(n+2, 0), a(n+1)/2):
seq(a(n), n=0..24);  # Alois P. Heinz, Jun 15 2023

Mathematica

a[n_] := 2^Mod[n, 2]*Abs[PolyLog[-(n + 3 - Mod[n, 2]), I]];
Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Dec 02 2023, after Mikhail Kurkov *) [verification needed]

Prog

(PARI) a(n) = 2^(n%2)*abs(polylog(-(n + 3 - n%2), I)) \\ Mikhail Kurkov, Jun 13 2023 [verification needed]

Crossrefs

Cf. A000111, A002735.

Sequence in context: A092978 A280777 A013516 * A101059 A191999 A101658

Adjacent sequences: A259685 A259686 A259687 * A259689 A259690 A259691

Keyword

nonn,changed

Author

N. J. A. Sloane, Jul 04 2015

Extensions

More terms from Mikhail Kurkov, Jun 13 2023 [verification needed]

a(0)=1 prepended by Alois P. Heinz, Jun 13 2023

Status

approved