A260786 Twice the Euler or up/down numbers A000111.

2, 2, 2, 4, 10, 32, 122, 544, 2770, 15872, 101042, 707584, 5405530, 44736512, 398721962, 3807514624, 38783024290, 419730685952, 4809759350882, 58177770225664, 740742376475050, 9902996106248192, 138697748786275802, 2030847773013704704, 31029068327114173810, 493842960380415967232

Offset

0,1

Links

Table of n, a(n) for n=0..25.

S. T. Thompson, Problem E754: Skew Ordered Sequences, Amer. Math. Monthly, 54 (1947), 416-417. [Annotated scanned copy]

Formula

a(0)=a(1)=2; thereafter a(n) = (1/4)*Sum_{k=1..n} binomial(n-1, k-1)*a(k-1)*a(n-k).

Maple

f:=proc(n) option remember;
if n <= 1 then 2 else (1/4)*add(binomial(n-1, k-1)*f(k-1)*f(n-k), k=1..n); fi;
end;
[seq(f(n), n=0..30)];

Prog

(Python)
from itertools import accumulate, islice
def A260786_gen(): # generator of terms
    yield from (2, 2)
    blist = (0, 2)
    while True:
        yield (blist := tuple(accumulate(reversed(blist), initial=0)))[-1]
A260786_list = list(islice(A260786_gen(), 30)) # Chai Wah Wu, Apr 17 2023

Crossrefs

Cf. A000111.

Apart from initial terms, same as A001250.

Sequence in context: A307522 A130707 A131562 * A067920 A107902 A142974

Adjacent sequences: A260783 A260784 A260785 * A260787 A260788 A260789

Keyword

nonn

Author

N. J. A. Sloane, Aug 04 2015

Status

approved