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 A217144 Alternating sums of squares of Bell numbers (A000110). 1
 1, 0, 4, 21, 204, 2500, 38709, 730420, 16409180, 430786429, 13019414196, 447437830704, 17306961847705, 746907935199264, 35695643204860420, 1876878693983656605, 107956500727342113004, 6758630146906528885412, 458470139353155531447869 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..18. FORMULA a(n) = Sum_{k=0..n} (-1)^(n-k)*Bell(k)^2. PROG (Maxima) makelist(sum((-1)^(n-k)*belln(k)^2, k, 0, n), n, 0, 30); (Python) from itertools import accumulate, islice def A217144_gen(): # generator of terms yield 1 blist, b, c, f = (1, ), 1, 1, 1 while True: blist = list(accumulate(blist, initial=(b:=blist[-1]))) yield (f:=-f)*(c := c+f*b**2) A217144_list = list(islice(A217144_gen(), 20)) # Chai Wah Wu, Jun 22 2022 CROSSREFS Cf. A000110, A005001, A087650, A217143. Sequence in context: A360630 A041667 A286883 * A132684 A357857 A032074 Adjacent sequences: A217141 A217142 A217143 * A217145 A217146 A217147 KEYWORD nonn AUTHOR Emanuele Munarini, Sep 27 2012 STATUS approved

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Last modified July 13 12:36 EDT 2024. Contains 374284 sequences. (Running on oeis4.)