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 A121870 Monthly Problem 10791, second expression. 1
 1, 1, 2, 9, 61, 554, 6565, 96677, 1716730, 36072181, 881242577, 24674241834, 783024550969, 27896201305769, 1106485798248706, 48517267642373105, 2337333266369553253, 123040664089658462650, 7043260281573138384701, 436533086101058798529933 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS A. Fekete and G. Martin, Problem 10791, Amer. Math. Monthly, 108 (No. 2, 2001), 177-178. FORMULA a(n) = A121867(n)^2 + A121868(n)^2. From Gary W. Adamson, Jul 22 2011: (Start) sqrt(a(n)) = upper left term in M^n as to the modulus of a polar term; M = an infinite square production matrix in which a column of (i, i, i,...) is appended to the right of Pascal's triangle, as follows (with i = sqrt(-1)): 1, i, 0, 0, 0,... 1, 1, i, 0, 0,... 1, 2, 1, i, 0,... 1, 3, 3, 1, i,... ... (End) a(n) = |B_n(i)|^2, where B_n(x) is the n-th Bell polynomial, i = sqrt(-1) is the imaginary unit. - Vladimir Reshetnikov, Oct 15 2017 EXAMPLE a(4) = 61 = square of upper left term of M^4, = the square of (sqrt(61)Angle 140.194....), where the modulus is squared, getting 61. MAPLE A121870a:= proc(a) local i, t: i:=1: t:=0: for i to 100 do t:=t+evalf((i^(a-1))*(I)^i/(i)!): od: RETURN(round(abs(t^2))): end: a:= A121870a(n); # Russell Walsmith, Apr 18 2008 # Alternate: seq(abs(BellB(n, I))^2, n=0..30); # Robert Israel, Oct 15 2017 MATHEMATICA Table[Abs[BellB[n, I]]^2, {n, 0, 20}] (* Vladimir Reshetnikov, Oct 15 2017 *) CROSSREFS Cf. A121869, A024429, A024430, A121867, A121868. Sequence in context: A107883 A088182 A006155 * A268450 A146887 A173498 Adjacent sequences:  A121867 A121868 A121869 * A121871 A121872 A121873 KEYWORD nonn AUTHOR N. J. A. Sloane, Sep 05 2006 STATUS approved

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Last modified May 24 00:38 EDT 2019. Contains 323528 sequences. (Running on oeis4.)