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A024716 a(n) = sum of S(i,j), 1<=j<=i<=n, where S(i,j) are Stirling numbers of the second kind. 5
1, 3, 8, 23, 75, 278, 1155, 5295, 26442, 142417, 820987, 5034584, 32679021, 223578343, 1606536888, 12086679035, 94951548839, 777028354998, 6609770560055, 58333928795427, 533203744952178, 5039919483399501, 49191925338483847, 495150794633289136 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums of triangle A137649 - Gary W. Adamson, Feb 01 2008

LINKS

T. D. Noe, Table of n, a(n) for n=1..100

FORMULA

If offset is 0, a(n) = Sum_{i=0..n} binomial(n+1, i+1)*Bell(i) [cf. A000110].

Partial sums of Bell numbers. - Vladeta Jovovic, Mar 16 2003

G.f.: G(0)/(1-x) where G(k) = 1 - 2*x*(k+1)/((2*k+1)*(2*x*k+x-1) - x*(2*k+1)*(2*k+3)*(2*x*k+x-1)/(x*(2*k+3) - 2*(k+1)*(2*x*k+2*x-1)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Dec 20 2012

G.f.: ( G(0) - 1 )/(1-x) where G(k) =  1 + (1-x)/(1-x*(k+1))/(1-x/(x+(1-x)/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 21 2013

G.f.: (S-1)/(1-x) where S=1/(1-x)*sum(k>=0, ( 1 + (1-x)/(1-x-x*k) )*x^k/prod(i=1..k-1, (1-x-x*i) ) ). - Sergei N. Gladkovskii, Jan 22 2013

G.f.: ((G(0)-2)/(2*x-1)-1)/(1-x)/x where G(k) =  2 - 1/(1-k*x)/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 26 2013

G.f.: 1/(G(0)-x)/(1-x) where G(k) = 1 - x*(k+1)/(1 - x/G(k+1) ); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 26 2013

MAPLE

with (combinat):seq(sum(sum(stirling2(k, j), j=1..k), k=1..n), n=1..23); - Zerinvary Lajos, Dec 04 2007

MATHEMATICA

Accumulate[Table[BellB[n], {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2011 *)

CROSSREFS

Equals A005001(n+1) - 1. First column of triangle A101908.

Cf. A137649.

Sequence in context: A148778 A099265 A099266 * A189359 A125782 A047143

Adjacent sequences:  A024713 A024714 A024715 * A024717 A024718 A024719

KEYWORD

nonn,easy,nice

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified February 25 00:39 EST 2018. Contains 299630 sequences. (Running on oeis4.)