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# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a346432 Showing 1-1 of 1 %I A346432 #10 Jul 18 2021 07:10:05 %S A346432 1,2,14,144,1968,33600,688320,16450560,449326080,13806858240, %T A346432 471395635200,17703899136000,725338710835200,32193996432998400, %U A346432 1538840509503897600,78808952068374528000,4305129487814098944000,249876735246162984960000,15356385691181506363392000 %N A346432 a(0) = 1; a(n) = n! * Sum_{k=0..n-1} (n-k+1) * a(k) / k!. %F A346432 E.g.f.: 1 / (2 - 1 / (1 - x)^2). %F A346432 E.g.f.: 1 / (1 - Sum_{k>=1} (k+1) * x^k). %F A346432 a(0) = 1, a(1) = 2, a(2) = 14; a(n) = 4 * n * a(n-1) - 2 * n * (n-1) * a(n-2). %F A346432 a(n) = Sum_{k=0..n} (-1)^(n-k) * Stirling1(n,k) * 2^k * A000670(k). %F A346432 a(n) = n! * A003480(n). %t A346432 a[0] = 1; a[n_] := a[n] = n! Sum[(n - k + 1) a[k]/k!, {k, 0, n - 1}]; Table[a[n], {n, 0, 18}] %t A346432 nmax = 18; CoefficientList[Series[1/(2 - 1/(1 - x)^2), {x, 0, nmax}], x] Range[0, nmax]! %t A346432 Table[Sum[(-1)^(n - k) StirlingS1[n, k] 2^k HurwitzLerchPhi[1/2, -k, 0]/2, {k, 0, n}], {n, 0, 18}] %o A346432 (PARI) my(x='x+O('x^25)); Vec(serlaplace(1 / (2 - 1 / (1 - x)^2))) \\ _Michel Marcus_, Jul 18 2021 %Y A346432 Cf. A000670, A001339, A002866, A003480, A007840, A052555, A052567, A136658, A216794, A308939, A346433. %K A346432 nonn %O A346432 0,2 %A A346432 _Ilya Gutkovskiy_, Jul 17 2021 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE