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A091346 Binomial convolution of A069321(n), where A069321(0)=0, with the sequence of all ones alternating in sign. 3
0, 1, 3, 19, 135, 1171, 11823, 136459, 1771815, 25561891, 405658143, 7022891899, 131714587095, 2660335742611, 57570797744463, 1328913670495339, 32592691757283975, 846383665814211331, 23200396829832102783 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n)=Sum(C(n, k)(-1)^(n-k)Sum(i!i Stirling2(k, i), i=1, .., k), k=0, .., n).

E.g.f.: ((exp(x)-1)/(2-exp(x))^2)*exp(-x).

a(n) = (A000670(n+1)+(-1)^(n+1))/4. - Vladeta Jovovic, Jan 17 2005

G.f.: x/(1+x)/Q(0), where Q(k) = 1 - x*(3*k+4) - 2*x^2*(k+1)*(k+3)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 03 2013

MATHEMATICA

Table[Sum[Binomial[n, k](-1)^(n-k)Sum[i!i StirlingS2[k, i], {i, 1, k}], {k, 0, n}], {n, 0, 20}]

CROSSREFS

Cf. A083410.

Sequence in context: A226459 A256092 A074567 * A035086 A215852 A105797

Adjacent sequences:  A091343 A091344 A091345 * A091347 A091348 A091349

KEYWORD

easy,nonn

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Jan 02 2004

STATUS

approved

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Last modified December 2 13:03 EST 2016. Contains 278678 sequences.