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A309619
a(n) = Sum_{k=0..floor(n/2)} k! * (n - 2*k)!.
5
1, 1, 3, 7, 28, 128, 754, 5178, 41124, 368220, 3670872, 40290744, 482716896, 6267697920, 87664818960, 1313983544400, 21010949076960, 357007805477280, 6423473819220480, 122003441554176000, 2439346762501367040, 51213306647556506880, 1126446562222595147520
OFFSET
0,3
LINKS
FORMULA
G.f.: B(x)*B(x^2), where B(x) is g.f. of A000142.
a(n) ~ n! * (1 + 1/n^2 + 1/n^3 + 3/n^4 + 13/n^5 + 57/n^6 + 271/n^7 + 1467/n^8 + 8905/n^9 + 58965/n^10 + ...), for coefficients see A326984.
MATHEMATICA
nmax = 25; CoefficientList[Series[Sum[k!*x^k, {k, 0, nmax}]*Sum[k!*x^(2*k), {k, 0, nmax}], {x, 0, nmax}], x]
Table[Sum[k!*(n-2*k)!, {k, 0, Floor[n/2]}], {n, 0, 25}]
PROG
(PARI) a(n) = sum(k=0, n\2, k! * (n - 2*k)!); \\ Michel Marcus, Dec 08 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 10 2019
STATUS
approved