A099977 - OEIS

%I #15 Jun 22 2022 14:44:59

%S 1,5,52,877,21147,678570,27644437,1382958545,82864869804,

%T 5832742205057,474869816156751,44152005855084346,4638590332229999353,

%U 545717047936059989389,71339801938860275191172

%N Bisection of Bell numbers, A000110.

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

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

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

%o (Python)

%o from itertools import accumulate, islice

%o def A099977_gen(): # generator of terms

%o     yield 1

%o     blist, b = (1,2), 1

%o     while True:

%o         for _ in range(2):

%o             blist = list(accumulate(blist, initial=(b:=blist[-1])))

%o         yield b

%o A099977_list = list(islice(A099977_gen(),30)) # _Chai Wah Wu_, Jun 22 2022

%Y Cf. A000110, A020557.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Nov 19 2004

%E More terms from _Emeric Deutsch_, Dec 07 2004