0,3

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 2009: (Start)

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.

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

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

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.

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

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

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]

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)

Adjacent sequences: A002772 A002773 A002774 this_sequence A002776 A002777 A002778

Sequence in context: A081899 A057970 A154235 this_sequence A079754 A142703 A138403

nonn,new

N. J. A. Sloane (njas(AT)research.att.com).