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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 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-François 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.)