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A265023 Second order complementary Bell numbers. 2
1, -1, 2, -4, 9, -22, 54, -139, 372, -948, 2607, -7388, 16058, -58957, 174854, 210448, 4345025, -2008714, -165872030, -1756557123, -6144936528, 60244093040, 1164910003567, 8228177887688, -10562519450714, -967088274083133, -11322641425582454, -37483806372774364 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..27.

MATHEMATICA

nmax = 27;

A = Exp[x] + O[x]^(nmax - 1);

B = Exp[1 - Integrate[A, x]]/E;

c = Exp[1 - Integrate[B, x]]/E;

CoefficientList[c, x] Range[0, nmax]! (* Jean-Fran├žois Alcover, Jul 12 2019, from PARI *)

PROG

(Sage)

# The function bell_transform is defined in A264428.

def A265023_list(len):

    uno = [1]*len

    complementary_bell_numbers = [sum((-1)^n*b for (n, b) in enumerate (bell_transform(n, uno))) for n in range(len)]

    complementary_bell_numbers2 = [sum((-1)^n*b for (n, b) in enumerate (bell_transform(n, complementary_bell_numbers))) for n in range(len)]

    return complementary_bell_numbers2

print A265023_list(28)

(PARI)

\\ For n>28 precision has to be adapted as needed!

A = exp('x + O('x^33) );

B = exp(1 - intformal(A) )/exp(1);

C = exp(1 - intformal(B) )/exp(1);

round(Vec(serlaplace(C)))

CROSSREFS

Cf. A000587 (complementary Bell numbers), A264428.

Sequence in context: A048211 A098719 A274289 * A290996 A198520 A115324

Adjacent sequences:  A265020 A265021 A265022 * A265024 A265025 A265026

KEYWORD

sign

AUTHOR

Peter Luschny, Dec 03 2015

STATUS

approved

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Last modified November 15 14:06 EST 2019. Contains 329149 sequences. (Running on oeis4.)