cp's OEIS Frontend

A265023 Second order complementary Bell numbers.

%I A265023 #16 Mar 28 2020 05:28:16
%S A265023 1,-1,2,-4,9,-22,54,-139,372,-948,2607,-7388,16058,-58957,174854,
%T A265023 210448,4345025,-2008714,-165872030,-1756557123,-6144936528,
%U A265023 60244093040,1164910003567,8228177887688,-10562519450714,-967088274083133,-11322641425582454,-37483806372774364
%N A265023 Second order complementary Bell numbers.
%t A265023 nmax = 27;
%t A265023 A = Exp[x] + O[x]^(nmax - 1);
%t A265023 B = Exp[1 - Integrate[A, x]]/E;
%t A265023 c = Exp[1 - Integrate[B, x]]/E;
%t A265023 CoefficientList[c, x] Range[0, nmax]! (* _Jean-François Alcover_, Jul 12 2019, from PARI *)
%o A265023 (Sage) # uses[bell_transform from A264428]
%o A265023 def A265023_list(len):
%o A265023     uno = [1]*len
%o A265023     complementary_bell_numbers = [sum((-1)^n*b for (n, b) in enumerate (bell_transform(n, uno))) for n in range(len)]
%o A265023     complementary_bell_numbers2 = [sum((-1)^n*b for (n, b) in enumerate (bell_transform(n, complementary_bell_numbers))) for n in range(len)]
%o A265023     return complementary_bell_numbers2
%o A265023 print(A265023_list(28))
%o A265023 (PARI)
%o A265023 \\ For n>28 precision has to be adapted as needed!
%o A265023 A = exp('x + O('x^33) );
%o A265023 B = exp(1 - intformal(A) )/exp(1);
%o A265023 C = exp(1 - intformal(B) )/exp(1);
%o A265023 round(Vec(serlaplace(C)))
%Y A265023 Cf. A000587 (complementary Bell numbers), A264428.
%K A265023 sign
%O A265023 0,3
%A A265023 _Peter Luschny_, Dec 03 2015