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 A305405 Expansion of Sum_{k>=0} k!!*x^k/Product_{j=1..k} (1 - j*x). 1
 1, 1, 3, 10, 41, 201, 1126, 7043, 48603, 366298, 2987189, 26163501, 244654150, 2430411335, 25539609327, 282834656434, 3290175964577, 40089424302657, 510340938343270, 6772086558823547, 93481666812344979, 1339885322519303434, 19907413622297965373, 306126204811557339045 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Stirling transform of A006882. LINKS N. J. A. Sloane, Transforms Eric Weisstein's World of Mathematics, Stirling Transform FORMULA E.g.f.: 1 + exp((exp(x) - 1)^2/2)*(exp(x) - 1)*(1 + sqrt(Pi/2)*erf((exp(x) - 1)/sqrt(2))). a(n) = Sum_{k=0..n} Stirling2(n,k)*k!!. MATHEMATICA nmax = 23; CoefficientList[Series[Sum[k!! x^k/Product[1 - j x, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x] nmax = 23; CoefficientList[Series[1 + Exp[(E^x - 1)^2/2] (Exp[x] - 1) (1 + Sqrt[Pi/2] Erf[(Exp[x] - 1)/Sqrt[2]]), {x, 0, nmax}], x] Range[0, nmax]! Table[Sum[StirlingS2[n, k] k!!, {k, 0, n}], {n, 0, 23}] CROSSREFS Cf. A000670, A004123, A006882, A305404. Sequence in context: A236407 A000248 A245504 * A030927 A002627 A030802 Adjacent sequences:  A305402 A305403 A305404 * A305406 A305407 A305408 KEYWORD nonn AUTHOR Ilya Gutkovskiy, May 31 2018 STATUS approved

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Last modified February 26 17:19 EST 2020. Contains 332293 sequences. (Running on oeis4.)