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 A340838 a(n) = (1/2) * Sum_{k>=0} (k*(k + n))^n / 2^k. 0
 1, 4, 139, 11928, 1909787, 491329088, 185373016419, 96425597012608, 66139668570414571, 57840395870803141632, 62813828698519808489915, 82933938539372018962724864, 130828514220436815006398809563, 243020960809424084526916839817216, 525038425527430196237626528753654867 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) = Sum_{k=0..n} binomial(n,k) * A000670(2*n-k) * n^k. MATHEMATICA Table[(1/2) Sum[(k (k + n))^n/2^k, {k, 0, Infinity}], {n, 0, 14}] Join[{1}, Table[(1/2) Sum[Binomial[n, k] HurwitzLerchPhi[1/2, k - 2 n, 0] n^k, {k, 0, n}], {n, 1, 14}]] CROSSREFS Cf. A000670, A098696, A249938, A292916, A340822. Sequence in context: A089666 A029850 A221675 * A291450 A093981 A055304 Adjacent sequences: A340835 A340836 A340837 * A340839 A340840 A340841 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jan 23 2021 STATUS approved

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Last modified March 24 14:56 EDT 2023. Contains 361479 sequences. (Running on oeis4.)