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A370510
Expansion of Sum_{k>=0} k! * ( x * (1+x^3) )^k.
3
1, 1, 2, 6, 25, 124, 738, 5136, 40922, 367218, 3664224, 40240560, 482278326, 6263414736, 87618506160, 1313435465280, 21003904630824, 356910121855320, 6422020465846320, 121980351190294800, 2438956634267865720, 51206322309647263200, 1126314497201852150640
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..floor(n/4)} (n-3*k)! * binomial(n-3*k,k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x*(1+x^3))^k))
(PARI) a(n) = sum(k=0, n\4, (n-3*k)!*binomial(n-3*k, k));
CROSSREFS
Cf. A370508.
Sequence in context: A321186 A291558 A357902 * A370511 A074010 A352660
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Feb 20 2024
STATUS
approved