A358609 a(n) = Sum_{k=0..floor(n/4)} (-1)^k * (n-4*k)!.
1, 1, 2, 6, 23, 119, 718, 5034, 40297, 362761, 3628082, 39911766, 478961303, 6226658039, 87174663118, 1307634456234, 20922310926697, 355681201437961, 6402286531064882, 121643792774375766, 2432881085865713303, 51090586490508002039, 1123994325491076615118
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..449
Programs
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PARI
a(n) = sum(k=0, n\4, (-1)^k*(n-4*k)!);
Formula
a(n) = n * a(n-1) - a(n-4) + n * a(n-5) for n > 4.
a(n) ~ n! * (1 - 1/n^4 - 6/n^5 - 25/n^6 - 90/n^7 - 300/n^8 - 938/n^9 - 2563/n^10 - ...). - Vaclav Kotesovec, Nov 25 2022