A024189 a(n) = ((n+3)!/2)*Sum_{k=1..n} (-1)^(k+1)/(k+3).

3, 3, 78, 186, 4008, 15912, 340560, 1931760, 43139520, 321312960, 7611891840, 70589232000, 1783264896000, 19854108288000, 535217663232000, 6967948748544000, 200181525175296000, 2987361024592896000, 91267413626898432000, 1537150149529860096000, 49817611958159130624000

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, Harmonic Number.

Formula

a(n) = ((n+3)!/12)*(5 - 6*log(2) + 3*(-1)^n*(psi((n+4)/2) - psi((n+5)/2))), psi(x) is the digamma function. - G. C. Greubel, Jan 02 2020

Maple

seq( (n+3)!*(5 + 6*add((-1)^k/k, k=1..n+3))/12, n=1..25); # G. C. Greubel, Jan 02 2020

Mathematica

Table[(n+3)!*(5 + 6*Sum[(-1)^k/k, {k, n+3}])/12, {n, 25}] (* G. C. Greubel, Jan 02 2020 *)

Prog

(PARI) a(n) = (n+3)!/2*sum(x=1, n, (-1)^(x+1)/(x+3)) \\ Michel Marcus, Mar 21 2013
(Magma) [Factorial(n+3)*(5 + 6*(&+[(-1)^k/k: k in [1..n+3]]))/12: n in [1..25]]; // G. C. Greubel, Jan 02 2020
(Sage) [factorial(n+3)*(5 + 6*sum((-1)^k/k for k in (1..n+3)))/12 for n in (1..25)] # G. C. Greubel, Jan 02 2020
(GAP) List([1..25], n-> Factorial(n+3)*(5 + 6*Sum([1..n+3], k-> (-1)^k/k))/12 ); # G. C. Greubel, Jan 02 2020

Crossrefs

Cf. A024188.

Sequence in context: A333827 A213137 A260076 * A217542 A007451 A087542

Adjacent sequences: A024186 A024187 A024188 * A024190 A024191 A024192

Keyword

nonn

Author

Clark Kimberling

Extensions

Terms a(14) and beyond from Andrew Howroyd, Jan 01 2020

Status

approved