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A122486 a(n) = Sum_{k=0..n} |Stirling1(n,k)|*Bell(k)^2. 0
1, 1, 5, 39, 425, 6053, 107735, 2321469, 59152987, 1750362419, 59286010621, 2271617296347, 97502863649141, 4649359584613201, 244550369307356039, 14101227268075911837, 886551391533830227267, 60482082002935189216499 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums of the absolute values of the triangle of Stirling1(n,k)*Bell(k)^2:

  1;

  0,    1;

  0,   -1,     4;

  0,    2,   -12,    25;

  0,   -6,    44,  -150,     225;

  0,   24,  -200,   875,   -2250,   2704;

  0, -120,  1096, -5625,   19125, -40560,   41209;

  0,  720, -7056, 40600, -165375, 473200, -865389, 769129;

  ... - R. J. Mathar, Jan 27 2017

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = exp(-2)*Sum_{r,s>=0} [r*s]^n/(r!*s!), where [m]^n = m*(m+1)*...*(m+n-1) is the rising factorial.

E.g.f.: Sum_{n>=0} exp( 1/(1-x)^n - 2 ) / n!. - Paul D. Hanna, Jul 25 2018

MAPLE

with(combinat): seq(sum(abs(stirling1(n, k))*bell(k)^2, k=0..n), n=0..19); # Emeric Deutsch, Oct 08 2006

CROSSREFS

Cf. A000110, A059849.

Sequence in context: A024216 A127189 A121354 * A187739 A199244 A322884

Adjacent sequences:  A122483 A122484 A122485 * A122487 A122488 A122489

KEYWORD

nonn,easy

AUTHOR

Vladeta Jovovic, Sep 15 2006, Sep 19 2006

EXTENSIONS

More terms from Emeric Deutsch, Oct 08 2006

STATUS

approved

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Last modified April 9 17:09 EDT 2020. Contains 333361 sequences. (Running on oeis4.)