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A326324 a(n) = A_{5}(n) where A_{m}(x) are the Eulerian polynomials as defined in A326323. 5
1, 1, 6, 46, 456, 5656, 84336, 1467376, 29175936, 652606336, 16219458816, 443419545856, 13224580002816, 427278468668416, 14867050125981696, 554245056343668736, 22039796215883268096, 931198483176870608896, 41658202699736550014976, 1967160945260218035798016 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

See A326323 for the more general formulas.

LINKS

Table of n, a(n) for n=0..19.

MAPLE

seq(add(combinat:-eulerian1(n, k)*5^k, k=0..n), n=0..20);

# Alternative:

egf := 4/(5 - exp(4*x)): ser := series(egf, x, 21):

seq(k!*coeff(ser, x, k), k=0..20);

MATHEMATICA

a[1] := 1; a[n_] := 4^(n + 1)/5 HurwitzLerchPhi[1/5, -n, 0];

Table[a[n], {n, 0, 20}]

(* Alternative: *)

s[n_] := Sum[StirlingS2[n, j] 4^(n - j) j!, {j, 0, n}];

Table[s[n], {n, 0, 20}]

CROSSREFS

Cf. A173018, A000012, A000142, A000670, A122704, A255927, A326323.

Sequence in context: A261499 A001829 A006386 * A215084 A232058 A331704

Adjacent sequences:  A326321 A326322 A326323 * A326325 A326326 A326327

KEYWORD

nonn

AUTHOR

Peter Luschny, Jun 27 2019

EXTENSIONS

Corrected after notice from Jean-Fran├žois Alcover by Peter Luschny, Jul 13 2019

STATUS

approved

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Last modified August 5 18:57 EDT 2021. Contains 346488 sequences. (Running on oeis4.)