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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

Table of n, a(n) for n=0..19.

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.)