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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 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 STATUS approved

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Last modified October 14 06:55 EDT 2019. Contains 327995 sequences. (Running on oeis4.)