A394078 a(n) = Sum_{k=0..n} (-1)^(k + 1) * k^(n - k) * Gamma(k, -k) / exp(k). Row sums of A393142.

1, 1, 2, 8, 54, 519, 6397, 96172, 1706424, 34904925, 808662337, 20928958434, 598464096008, 18737698303219, 637544979358213, 23423517214147512, 924197264434029488, 38975247881426173689, 1749531623930002416225, 83286004855369026615166, 4191066886993961276317856

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Prog

(Python)
from mpmath import mp, gammainc, exp, nint
def a(n: int) -> int:
    if n == 0: return 1
    mp.dps = 50
    val = sum((-1)**(k + 1) * k**(n - k) * gammainc(k, -k) / exp(k) for k in range(1, n + 1))
    return int(nint(val))
print([a(n) for n in range(21)])

Crossrefs

Cf. A393142.

Sequence in context: A375224 A365599 A013499 * A199576 A005155 A133316

Adjacent sequences: A394075 A394076 A394077 * A394079 A394080 A394081

Keyword

nonn

Author

Peter Luschny, Mar 09 2026

Status

approved