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 A094422 Antidiagonal sums of array A094416. 4
 1, 5, 26, 174, 1531, 17275, 243092, 4165260, 85133685, 2039546785, 56447550542, 1783865468186, 63766726231791, 2558290237404919, 114418196763735112, 5670168958036693976, 309630356618418661737, 18536683645526372648445 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..310 FORMULA a(n) = Sum_{k=1..n} Bo(n-k+1, k), where Bo(r, n) = A094416(r, n). MATHEMATICA Table[Sum[Sum[j!*(n - k + 1)^j*StirlingS2[k, j], {j, 0, n}], {k, 1, n}], {n, 1, 20}] (* Vaclav Kotesovec, Jul 23 2018 *) PROG (Magma) A094422:= func< n | (&+[(&+[Factorial(j)*(n-k+1)^j*StirlingSecond(k, j): j in [0..n]]): k in [1..n]]) >; [A094422(n): n in [1..25]]; // G. C. Greubel, Jan 11 2024 (SageMath) def f(n, k, j): return factorial(j)*(n-k+1)^j*stirling_number2(k, j) def A094422(n): return sum(sum(f(n, k, j) for j in range(n+1)) for k in range(1, n+1)) [A094422(n) for n in range(1, 26)] # G. C. Greubel, Jan 11 2024 CROSSREFS Cf. A094416. Sequence in context: A090226 A355672 A356597 * A346545 A179513 A302896 Adjacent sequences: A094419 A094420 A094421 * A094423 A094424 A094425 KEYWORD nonn AUTHOR Ralf Stephan, May 02 2004 STATUS approved

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Last modified September 17 23:36 EDT 2024. Contains 375991 sequences. (Running on oeis4.)