A128062 - OEIS

A128062

a(n) = denominator of b(n), where sum{m>=0} b(m)*x^m/m! = x/(sum{m>=1} H(m) x^m/ m!) = exp(-x)*x/(sum{m>=1} x^m (-1)^(m+1)/(m!*m)). (H(m) = sum{k=1 to m} 1/k.).

%I #11 Dec 29 2023 10:58:28

%S 1,4,72,96,21600,17280,5080320,322560,326592000,145152000,63228211200,

%T 22992076800,1298164008960000,292919058432000,11298306539520000,

%U 273898340352000,48978158848819200000,886482513100800000

%N a(n) = denominator of b(n), where sum{m>=0} b(m)*x^m/m! = x/(sum{m>=1} H(m) x^m/ m!) = exp(-x)*x/(sum{m>=1} x^m (-1)^(m+1)/(m!*m)). (H(m) = sum{k=1 to m} 1/k.).

%F b(0)=1. b(n) = -sum{k=1 to n} binomial(n,k) H(k+1) b(n-k)/(k+1).

%e 1/(1 + x * 3/(2 * 2) + x^2 * 11/(6 * 6) + x^3 * 25/(12 * 24) +...) = 1 -x * 3/4 + x^2 * 37/72 -x^3 * 29/96 ...

%t b[0] = 1;b[n_] := b[n] = -Sum[Binomial[n, k] *HarmonicNumber[k + 1]*b[n - k]/(k + 1), {k, n}];Denominator[Array[b, 20, 0]] (* _Ray Chandler_, Feb 19 2007 *)

%Y Cf. A128061.

%K frac,nonn

%O 0,2

%A _Leroy Quet_, Feb 13 2007

%E Extended by _Ray Chandler_, Feb 19 2007