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A121886 a(n) = (1/n!)* Sum_{k=0..n} |Stirling1(n,k)|*A122399(k). 2
1, 1, 5, 40, 444, 6324, 110023, 2261576, 53632424, 1441341350, 43290170494, 1437020742408, 52243864528990, 2064488610832106, 88106523694973953, 4038627301344466648, 197888243609535940091, 10321811633042512528240 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of square matrices with nonnegative integer entries and without zero rows such that sum of all entries is equal to n. - Vladeta Jovovic, Mar 04 2008

LINKS

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

FORMULA

G.f.: Sum_{n>=0} ( 1/(1-x)^n - 1 )^n.

G.f.: Sum_{n>=0} (1-x)^n / (1 + (1-x)^n)^(n+1). - Paul D. Hanna, Sep 07 2018

a(n) ~ c * d^n * n! / sqrt(n), where d = A317855 = (1+exp(1/r))*r^2 = 3.161088653865428813830172202588132491726382774188556341627278..., r = 0.8737024332396683304965683047207192982139922672025395099... is the root of the equation exp(1/r)/r + (1+exp(1/r))*LambertW(-exp(-1/r)/r) = 0, and c = 0.38377369607518184186200387319561108... . - Vaclav Kotesovec, May 07 2014

EXAMPLE

G.f.: A(x) = 1 + x + 5*x^2 + 40*x^3 + 444*x^4 + 6324*x^5 +...

where

A(x) = 1 + (1/(1-x) - 1) + (1/(1-x)^2 - 1)^2 + (1/(1-x)^3 - 1)^3 + ...

Also,

A(x) = 1/2 + (1-x)/(1 + (1-x))^2 + (1-x)^2/(1 + (1-x)^2)^3 +  + (1-x)^3/(1 + (1-x)^3)^4 + (1-x)^4/(1 + (1-x)^4)^5 + ...

MATHEMATICA

Flatten[{1, Table[1/n!* Sum[Abs[StirlingS1[n, k]]*Sum[m^k*m!*StirlingS2[k, m], {m, 1, k}], {k, 0, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, May 07 2014 *)

PROG

(PARI) {a(n)=polcoeff(sum(m=0, n, (1/(1-x+x*O(x^n))^m-1)^m), n)}

CROSSREFS

Cf. A104209, A220352.

Sequence in context: A202477 A034000 A000359 * A282190 A052868 A292405

Adjacent sequences:  A121883 A121884 A121885 * A121887 A121888 A121889

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Aug 31 2006

EXTENSIONS

More terms from Max Alekseyev, Feb 01 2007

STATUS

approved

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Last modified April 11 18:00 EDT 2021. Contains 342888 sequences. (Running on oeis4.)