A265022 Row sums of the Bell transform of the complementary Bell numbers (A264435).

1, 1, 0, -2, -1, 12, 20, -113, -430, 1278, 10821, -10234, -317048, -384915, 10352420, 42836466, -340348905, -3180089128, 8045616512, 219303897655, 301713947470, -14401913182942, -84197219028827, 824481606288554, 11426928115546036, -23133559937561187

Offset: 0

Author

Peter Luschny, Dec 01 2015

Keywords

• sign

Links

• Peter Luschny, The Bell transform

Crossrefs

Cf. A000587 (complementary Bell numbers), A264428, A264435, A265023, A265024.

Programs

Mathematica

Table[Sum[BellY[n, k, BellB[Range[n] - 1, -1]], {k, 0, n}], {n, 0, 30}] (* Vladimir Reshetnikov, Nov 09 2016 *)

Sage

# uses[bell_transform from A264428]
def A265022_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)]
    return [sum(bell_transform(n, complementary_bell_numbers)) for n in range(len)]
A265022_list(26)