A099977 Bisection of Bell numbers, A000110.

1, 5, 52, 877, 21147, 678570, 27644437, 1382958545, 82864869804, 5832742205057, 474869816156751, 44152005855084346, 4638590332229999353, 545717047936059989389, 71339801938860275191172

Offset: 0

Author

N. J. A. Sloane, Nov 19 2004

Keywords

• nonn
• easy

Crossrefs

Cf. A000110, A020557.

Programs

Maple

G:=series(exp(exp(x)-1),x=0,50): seq((2*n-1)!*coeff(G,x^(2*n-1)),n=1..18);

Python

from itertools import accumulate, islice
def A099977_gen(): # generator of terms
    yield 1
    blist, b = (1,2), 1
    while True:
        for _ in range(2):
            blist = list(accumulate(blist, initial=(b:=blist[-1])))
        yield b
A099977_list = list(islice(A099977_gen(),30)) # Chai Wah Wu, Jun 22 2022

Formula

E.g.f.: exp(-1)*Sum_{n>=0} n*exp(n^2*x)/n!. - Vladeta Jovovic, Aug 24 2006

a(n) = exp(-1) * Sum_{k>=0} k^(2*n+1)/k!. - Ilya Gutkovskiy, Jun 13 2019

Extensions

More terms from Emeric Deutsch, Dec 07 2004