A394078 - OEIS

%I #6 Mar 10 2026 05:29:22

%S 1,1,2,8,54,519,6397,96172,1706424,34904925,808662337,20928958434,

%T 598464096008,18737698303219,637544979358213,23423517214147512,

%U 924197264434029488,38975247881426173689,1749531623930002416225,83286004855369026615166,4191066886993961276317856

%N a(n) = Sum_{k=0..n} (-1)^(k + 1) * k^(n - k) * Gamma(k, -k) / exp(k). Row sums of A393142.

%o (Python)

%o from mpmath import mp, gammainc, exp, nint

%o def a(n: int) -> int:

%o     if n == 0: return 1

%o     mp.dps = 50

%o     val = sum((-1)**(k + 1) * k**(n - k) * gammainc(k, -k) / exp(k) for k in range(1, n + 1))

%o     return int(nint(val))

%o print([a(n) for n in range(21)])

%Y Cf. A393142.

%K nonn

%O 0,3

%A _Peter Luschny_, Mar 09 2026