A122486 a(n) = Sum_{k=0..n} |Stirling1(n,k)|*Bell(k)^2.

1, 1, 5, 39, 425, 6053, 107735, 2321469, 59152987, 1750362419, 59286010621, 2271617296347, 97502863649141, 4649359584613201, 244550369307356039, 14101227268075911837, 886551391533830227267, 60482082002935189216499

Offset: 0

Author

Vladeta Jovovic, Sep 15 2006, Sep 19 2006

Keywords

• nonn
• easy

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

Crossrefs

Cf. A000110, A059849.

Programs

Maple

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

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

Extensions

More terms from Emeric Deutsch, Oct 08 2006