A086881 a(n) = (2*n)!*Sum[Sum[1/(i+j),{i,1,n}],{j,1,n}]

1, 34, 1788, 146256, 17485920, 2894002560, 635331029760, 178910029670400, 62920533840998400, 27042268338763776000, 13950701922125574144000, 8509745665997194493952000, 6059691013778107566981120000

Offset

1,2

Links

Table of n, a(n) for n=1..13.

Eric Weisstein's World of Mathematics, Hilbert Matrix.

Eric Weisstein's World of Mathematics, Harmonic Number.

Formula

a(n) = (2*n)!*((2*n+1)*Psi(2*n+2)-(2*n+2)*Psi(n+2)+1-gamma). limit(a(n)/(2*n)!/n, n=infinity)=2*ln2. - Vladeta Jovovic, Aug 24 2003

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

a(n) = (2n)! * ((2n+2)*H(2n+2) - 2(n+1)*H(n+1) - H(2n+1)), where H(n) is HarmonicNumber[n] = Sum[1/i, {i, 1, n}] = A001008(n)/A002805(n). - Alexander Adamchuk, Nov 01 2004

Example

a(2) = 4!*(1/(1+1)+1/(1+2)+1/(2+1)+1/(2+2)) = 24*(1/2+1/3+1/3+1/4)

Mathematica

Table[((2*n)!)*Sum[Sum[1/(a+b), {i, 1, n}], {j, 1, n}], {n, 1, 20}]

Crossrefs

Cf. A098118, A001008, A002805.

Sequence in context: A212033 A202297 A296673 * A212023 A056566 A335090

Adjacent sequences: A086878 A086879 A086880 * A086882 A086883 A086884

Keyword

nonn

Author

Alexander Adamchuk, Aug 21 2003

Status

approved