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A392717

Expansion of e.g.f. Series_Reversion(exp(x) - 1 - x^4).

1, -1, 2, 18, -336, 4080, -26160, -373464, 20187720, -497150160, 6744047760, 79240010784, -9375203058144, 375103520238720, -8411655884224320, -49887611181843264, 16526744933318894592, -970876437989727314304, 32065750181047673237760, -64082990645678091419136

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OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..300

FORMULA

a(n) = Sum_{k=0..floor((n-1)/3)} (4*k)!/k! * Stirling1(n+k,4*k+1).

E.g.f. A(x) satisfies A(x) = log(1 + x + A(x)^4).

E.g.f.: log(1 + B(x)), where B(x) is the e.g.f. of A392718.

MATHEMATICA

Table[Sum[(4*k)!/k!*StirlingS1[n+k, 4*k+1], {k, 0, Floor[(n-1)/3]}], {n, 1, 21}] (* Vincenzo Librandi, Feb 17 2026 *)

PROG