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A370378
Number of compositions of n where there are (2*k)! sorts of part k.
1
1, 2, 28, 824, 44080, 3837536, 496714432, 89388391808, 21308786907904, 6492490191541760, 2459980247094946816, 1134165248844198336512, 625104522913814858149888, 405845822590303335956701184, 306541019968859037778756157440
OFFSET
0,2
FORMULA
G.f.: 1 / (1 - Sum(k>=1} (2*k)! * x^k)).
a(0) = 1; a(n) = Sum_{k=1..n} (2*k)! * a(n-k).
a(n) ~ (2*n)! * (1 + 1/n^2 + 1/(2*n^3) + 4/n^4 + 91/(8*n^5) + 51/n^6 + 7951/(32*n^7) + 11147/(8*n^8) + 1122171/(128*n^9) + 983245/(16*n^10) + ...). - Vaclav Kotesovec, Feb 17 2024
MATHEMATICA
nmax = 15; CoefficientList[Series[1/(1 - Sum[(2*k)! * x^k, {k, 1, nmax}]), {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 17 2024 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(1/(1-sum(k=1, N, (2*k)!*x^k)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Feb 17 2024
STATUS
approved