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A002775 a(n) = n^2 * n!.
(Formerly M4540 N1927)
11
0, 1, 8, 54, 384, 3000, 25920, 246960, 2580480, 29393280, 362880000, 4829932800, 68976230400, 1052366515200, 17086945075200, 294226732800000, 5356234211328000, 102793666719744000, 2074369080655872000, 43913881247588352000, 973160803270656000000, 22531105497723863040000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Denominators in power series expansion of the higher order exponential integral E(x,m=2,n=1) - (gamma^2/2 + Pi^2/12 + gamma*log(x) + log(x)^2/2), n>0, see A163931. -_ Johannes W. Meijer_, Oct 16 2009

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..21.

J. D. H. Dickson, Discussion of two double series arising from the number of terms in determinants of certain forms, Proc. London Math. Soc., 10 (1879), 120-122.

J. D. H. Dickson, Discussion of two double series arising from the number of terms in determinants of certain forms, Proc. London Math. Soc., 10 (1879), 120-122. [Annotated scanned copy]

FORMULA

E.g.f.: x*(1+x)/(1-x)^3. - Vladeta Jovovic, Dec 01 2002

E.g.f.: x*A'(x) where A(x) is the e.g.f. for A001563. - Geoffrey Critzer, Jan 17 2012

Sum of all matrix elements M(i, j) = i/(i+j) multiplied by 2*n!. a(n) = 2*n! * Sum[Sum[i/(i+j), {i, 1, n}], {j, 1, n}] Example: a(2) = 2*2! * (1/(1+1) + 1/(1+2) + 2/(2+1) + 2/(2+2)) = 8. - Alexander Adamchuk, Oct 24 2004

MAPLE

with(combinat):for n from 0 to 15 do printf(`%d, `, n!/2*sum(2*n, k=1..n)) od: # Zerinvary Lajos, Mar 13 2007

seq(sum(sum(mul(k, k=1..n), l=1..n), m=1..n), n=0..21); # Zerinvary Lajos, Jan 26 2008

with (combstruct):a:=proc(m) [ZL, {ZL=Set(Cycle(Z, card>=m))}, labeled]; end: ZLL:=a(1):seq(count(ZLL, size=n)*n^2, n=0..21); # Zerinvary Lajos, Jun 11 2008

a:=n->add(0+add(n!, j=1..n), j=1..n):seq(a(n), n=0..21); # Zerinvary Lajos, Aug 27 2008

MATHEMATICA

nn=20; a=1/(1-x); Range[0, nn]! CoefficientList[Series[x D[x D[a, x], x], {x, 0, nn}], x] (* Geoffrey Critzer, Jan 17 2012 *)

CROSSREFS

Cf. A047922.

Cf. A163931 (E(x,m,n)), A001563 (n*n!), A091363 (n^3*n!), A091364 (n^4*n!). - Johannes W. Meijer, Oct 16 2009

Sequence in context: A287814 A201640 A263885 * A079754 A298985 A142703

Adjacent sequences:  A002772 A002773 A002774 * A002776 A002777 A002778

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 16 22:43 EST 2018. Contains 317275 sequences. (Running on oeis4.)