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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(14) and beyond from Andrew Howroyd, Jan 01 2020
STATUS
approved