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A002775
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n^2*n!.
(Formerly M4540 N1927)
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7
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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; internal format)
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OFFSET
| 0,3
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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*ln(x) + ln(x)^2/2), n>0, see A163931. - Johannes W. Meijer, Oct 16 2009
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REFERENCES
| 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.
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).
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FORMULA
| E.g.f.: x*(1+x)/(1-x)^3. - Vladeta Jovovic (vladeta(AT)eunet.rs), 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 (alex(AT)kolmogorov.com), Oct 24 2004
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MAPLE
| with(combinat):for n from 0 to 15 do printf(`%d, `, n!/2*sum(2*n, k=1..n)) od: - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 13 2007
seq(sum(sum(mul(k, k=1..n), l=1..n), m=1..n), n=0..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 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 (zerinvarylajos(AT)yahoo.com), Jun 11 2008
a:=n->add(0+add(n!, j=1..n), j=1..n):seq(a(n), n=0..21); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 27 2008]
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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 *)
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CROSSREFS
| Cf. A047922.
Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)
Cf. A163931 (E(x,m,n)), A001563 (n*n!), A091363 (n^3*n!), A091364 (n^4*n!).
(End)
Sequence in context: A057970 A154235 A201640 * A079754 A142703 A138403
Adjacent sequences: A002772 A002773 A002774 * A002776 A002777 A002778
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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