OFFSET
0,2
COMMENTS
a(n) is the n-th term of the main diagonal of iterated partial sums array of powers of n (see example).
FORMULA
a(n) = [x^n] 1/((1 - x)^n*(1 - n*x)).
a(n) ~ exp(1) * n^n. - Vaclav Kotesovec, Oct 16 2017
EXAMPLE
For n = 2 we have:
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0 1 [2] 3 4 5
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1, 2, 4, 8, 16, 32, ... A000079 (powers of 2)
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therefore a(2) = 11.
MATHEMATICA
Join[{1}, Table[Sum[n^(n - k) Binomial[n + k - 1, k], {k, 0, n}], {n, 1, 20}]]
Table[SeriesCoefficient[1/((1 - x)^n (1 - n x)), {x, 0, n}], {n, 0, 20}]
Join[{1, 2}, Table[n^(2 n)/(n - 1)^n - Binomial[2 n, n + 1] Hypergeometric2F1[1, 2 n + 1, n + 2, 1/n]/n, {n, 2, 20}]]
PROG
(PARI) a(n) = sum(k=0, n, n^(n-k)*binomial(n+k-1, k)); \\ Michel Marcus, Oct 12 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 12 2017
STATUS
approved