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A120732 Number of square matrices with nonnegative integer entries and without zero rows or columns such that sum of all entries is equal to n. 3
1, 1, 3, 15, 107, 991, 11267, 151721, 2360375, 41650861, 821881709, 17932031225, 428630422697, 11138928977049, 312680873171465, 9428701154866535, 303957777464447449, 10431949496859168189, 379755239311735494421 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..250

FORMULA

a(n) = (1/n!)*Sum_{k=0..n} (-1)^(n-k)*Stirling1(n,k)*A048144(k).

G.f.: Sum_{n>=0} Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*((1-x)^(-j)-1)^n.

a(n) ~ c * n! / (sqrt(n) * (log(2))^(2*n)), where c = 0.4670932578797312973586879293426... . - Vaclav Kotesovec, May 07 2014

In closed form, c = 2^(log(2)/2-2) / (log(2) * sqrt(Pi*(1-log(2)))). - Vaclav Kotesovec, May 03 2015

G.f.: Sum_{n>=0} (1-x)^n * (1 - (1-x)^n)^n. - Paul D. Hanna, Mar 26 2018

MATHEMATICA

Table[1/n!*Sum[(-1)^(n-k)*StirlingS1[n, k]*Sum[(m!)^2*StirlingS2[k, m]^2, {m, 0, k}], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, May 07 2014 *)

CROSSREFS

Cf. A104602.

Sequence in context: A120016 A074519 A105618 * A245835 A090351 A136221

Adjacent sequences:  A120729 A120730 A120731 * A120733 A120734 A120735

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Aug 18 2006

STATUS

approved

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Last modified August 18 04:26 EDT 2018. Contains 313821 sequences. (Running on oeis4.)