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 A360592 G.f.: Sum_{k>=0} (1 + k*x)^k * x^k. 16
 1, 1, 2, 5, 14, 44, 149, 543, 2096, 8539, 36444, 162380, 752181, 3612037, 17933038, 91843329, 484280386, 2624400428, 14595111277, 83178971707, 485218783724, 2893881790823, 17628815344600, 109585578277012, 694575012732989, 4485139961090153, 29486515600393930 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..760 FORMULA a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k) * (n-k)^k. a(n) ~ exp(exp(1/2)*sqrt(n/2) - 3*exp(1)/8) * n^(n/2) / 2^(n/2 + 1) * (1 + ((exp(1/2) + exp(-1/2))/2^(5/2) + 11*exp(3/2)/2^(9/2))/sqrt(n)). MAPLE N:= 40: S:= series(add((1+k*x)^k*x^k, k=0..N), x, N+1): seq(coeff(S, x, k), k=0..N); # Robert Israel, Feb 13 2023 MATHEMATICA nmax = 30; CoefficientList[Series[Sum[(1 + k*x)^k * x^k, {k, 0, nmax}], {x, 0, nmax}], x] Flatten[{1, Table[Sum[Binomial[n-k, k] * (n-k)^k, {k, 0, n/2}], {n, 1, 30}]}] PROG (PARI) {a(n) = polcoeff(sum(m=0, n, (1 + m*x)^m * x^m + x*O(x^n)), n)}; for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A360232, A092366, A187018, A360699, A360707. Sequence in context: A268419 A149883 A307786 * A363431 A149884 A149885 Adjacent sequences: A360589 A360590 A360591 * A360593 A360594 A360595 KEYWORD nonn AUTHOR Vaclav Kotesovec, Feb 13 2023 STATUS approved

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Last modified May 17 19:53 EDT 2024. Contains 372607 sequences. (Running on oeis4.)