A370378 Number of compositions of n where there are (2*k)! sorts of part k.

1, 2, 28, 824, 44080, 3837536, 496714432, 89388391808, 21308786907904, 6492490191541760, 2459980247094946816, 1134165248844198336512, 625104522913814858149888, 405845822590303335956701184, 306541019968859037778756157440

Offset

0,2

Links

Table of n, a(n) for n=0..14.

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

Cf. A051296, A010050, A370379.

Sequence in context: A372165 A090249 A264411 * A009256 A012725 A264637

Adjacent sequences: A370375 A370376 A370377 * A370379 A370380 A370381

Keyword

nonn,easy

Author

Seiichi Manyama, Feb 17 2024

Status

approved