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 A111885 Row sums of triangle A112492. 2
 1, 2, 5, 20, 152, 2542, 100326, 10194844, 2809233510, 2212797607312, 5359196565766782, 39928779843430949176, 1018129474625651322506886, 85890171235256453902613870992, 26477529277143069417959927152215342 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..55 FORMULA a(n) = Sum_{j=0..n} A112492(n, j), n >= 0. MATHEMATICA T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, (k+1)^(n-k)*T[n-1, k-1] + k!*T[n-1, k]]; a[n_]:= a[n]= Sum[T[n, k], {k, 0, n}]; (* T = A112492 *) Table[a[n], {n, 0, 40}] (* G. C. Greubel, Jul 24 2023 *) PROG (Magma) T:= func< n, k | (-1)*Factorial(k+1)^(n-k)*(&+[(-1)^j*Binomial(k+1, j)/j^(n-k) : j in [1..k+1]]) >; // T = A112492 A111885:= func< n | (&+[T(n, k): k in [0..n]]) >; [A111885(n): n in [0..40]]; // G. C. Greubel, Jul 24 2023 (SageMath) @CachedFunction def T(n, k): # T = A112492 if (k==0 or k==n): return 1 else: return (k+1)^(n-k)*T(n-1, k-1) + factorial(k)*T(n-1, k) def A111885(n): return sum(T(n, k) for k in range(n+1)) [A111885(n) for n in range(31)] # G. C. Greubel, Jul 24 2023 CROSSREFS Cf. A112492. Sequence in context: A140988 A136650 A229662 * A159320 A184730 A181076 Adjacent sequences: A111882 A111883 A111884 * A111886 A111887 A111888 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Sep 12 2005 STATUS approved

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Last modified February 27 18:50 EST 2024. Contains 370378 sequences. (Running on oeis4.)