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A376444
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x^2) - 1))^3 ).
1
1, 0, 0, 18, 0, 180, 23760, 2520, 1693440, 180033840, 107956800, 42093263520, 4131388800000, 7363478041920, 2262271571239680, 213613512570057600, 843365230060953600, 226557537882970694400, 20988751571439158707200, 154613821575430253836800, 38125864157166326661120000, 3508865828606684108929766400
OFFSET
0,4
FORMULA
E.g.f. A(x) satisfies A(x) = 1/(1 - x*A(x) * (exp(x^2*A(x)^2) - 1))^3.
a(n) = (3 * n!/(3n+3)!) * Sum_{k=0..floor(n/2)} (4*n-2*k+2)! * Stirling2(k,n-2*k)/k!.
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x^2)-1))^3)/x))
(PARI) a(n) = 3*n!*sum(k=0, n\2, (4*n-2*k+2)!*stirling(k, n-2*k, 2)/k!)/(3*n+3)!;
CROSSREFS
Cf. A375665.
Sequence in context: A052441 A375665 A375681 * A376442 A221394 A025602
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 22 2024
STATUS
approved