A231895 a(n) = 2*A000111(n+1) + A000111(n).

3, 3, 5, 12, 37, 138, 605, 3042, 17257, 108978, 758105, 5759322, 47439277, 421090218, 4006875605, 40686781602, 439122198097, 5019624693858, 60582649901105, 769831261587882, 10273367294485717, 143649246839399898, 2100196647406842605, 32044492213621026162, 509357494543973054137

Offset: 0

Author

N. J. A. Sloane, Nov 18 2013

Keywords

• nonn

Comments

It is clear from the Berry et al. article that they intended to consider 2*A000111(n+1) - A000111(n) (which is A104854), not 2*A000111(n+1) + A000111(n).

Links

• D. Berry, J. Broom, D. Dixon, and A. Flaherty, Umbral Calculus and the Boustrophedon Transform, 2013.

Crossrefs

Cf. A000111, A104854.

Programs

Python

from itertools import accumulate, islice
def A231895_gen(): # generator of terms
    yield 3
    blist = (0,1)
    while True:
        yield blist[-1]+2*(blist := tuple(accumulate(reversed(blist),initial=0)))[-1]
A231895_list = list(islice(A231895_gen(),40)) # Chai Wah Wu, Jun 14 2022

Formula

E.g.f.: 1 + (sec(x) + tan(x) + 1)*(sec(x) + tan(x)). - Sergei N. Gladkovskii, Jun 11 2015