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A252284 Exponential generating function exp(-x-x^2-x^3/3). 1
1, -1, -1, 3, 9, -21, -129, 111, 2577, 2871, -57249, -232101, 1175769, 11951523, -6313761, -542318841, -1778088159, 20647593711, 187318128447, -386536525389, -13793029404759, -41926398389541, 783578974052799, 7433562140085663, -22263437361406671, -767083139039850201 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..25.

FORMULA

a(n) = sum_{k=0..n} ((n!/k!)*(-1)^k * sum_{i=0..k} C(k,i)*C(k-i,n-2*i-k)/3^i).

E.g.f.: exp(-x-x^2-x^3/3).

Recurrence: a(n+3)+a(n+2)+2*(n+2)*a(n+1)+(n+2)*(n+1)*a(n)=0.

MAPLE

S:= series(exp(-x-x^2-x^3/3), x, 101):

seq(coeff(S, x, j)*j!, j=0..100); # Robert Israel, Dec 16 2014

MATHEMATICA

a[n_] := Sum[(n!/k!)(-1)^k Sum[Binomial[k, i]Binomial[k-i, n-2i-k]/3^i, {i, 0, k}], {k, 0, n}]; Table[a[n], {n, 0, 20}]

PROG

(Maxima) a(n) := sum((n!/k!)*(-1)^k*sum(binomial(k, i)*binomial(k-i, n-2*i-k)/3^i, i, 0, k), k, 0, n);

makelist(a(n), n, 0, 20);

(PARI) default(seriesprecision, 40); Vec(serlaplace( exp(-x-x^2-x^3/3))) \\ Michel Marcus, Dec 17 2014

CROSSREFS

Cf. A249015.

Sequence in context: A067645 A101474 A298836 * A259367 A193374 A191998

Adjacent sequences:  A252281 A252282 A252283 * A252285 A252286 A252287

KEYWORD

sign

AUTHOR

Emanuele Munarini, Dec 16 2014

STATUS

approved

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Last modified January 20 04:43 EST 2019. Contains 319323 sequences. (Running on oeis4.)