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A346890 Expansion of e.g.f. 1 / (1 - x^4 * exp(x) / 4!). 6
1, 0, 0, 0, 1, 5, 15, 35, 140, 1386, 12810, 92730, 589545, 4234945, 41832791, 483334215, 5401798220, 57262207380, 626438655900, 7740130412796, 107197808258745, 1546730804858085, 22360919412385015, 329241486278715395, 5121840342205301946 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
LINKS
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * binomial(k,4) * a(n-k).
a(n) ~ n! / ((1 + LambertW(3^(1/4)/2^(5/4))) * 4^(n + 1) * LambertW(3^(1/4)/2^(5/4))^n). - Vaclav Kotesovec, Aug 08 2021
a(n) = n! * Sum_{k=0..floor(n/4)} k^(n-4*k)/(24^k * (n-4*k)!). - Seiichi Manyama, May 13 2022
MATHEMATICA
nmax = 24; CoefficientList[Series[1/(1 - x^4 Exp[x]/4!), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Binomial[k, 4] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]
PROG
(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1-x^4*exp(x)/4!))) \\ Michel Marcus, Aug 06 2021
(PARI) a(n) = n!*sum(k=0, n\4, k^(n-4*k)/(24^k*(n-4*k)!)); \\ Seiichi Manyama, May 13 2022
CROSSREFS
Column k=4 of A351703.
Sequence in context: A091875 A056413 A032276 * A333932 A065780 A220480
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 06 2021
STATUS
approved

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Last modified April 16 03:28 EDT 2024. Contains 371696 sequences. (Running on oeis4.)