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A363396
a(n) = Sum_{k=0..n} 2^(n - k) * Sum_{j=0..k} binomial(k, j) * (2*j + 1)^n. Row sums of A363398.
1
1, 6, 68, 1280, 33104, 1089312, 43575104, 2053324800, 111402371328, 6839846858240, 468857355838464, 35494174578769920, 2941165554120118272, 264782344216518696960, 25734702989598729256960, 2685663154208346271121408, 299529317622247725531725824, 35554080433116190335493865472
OFFSET
0,2
FORMULA
a(n) ~ sqrt(1 + LambertW(exp(-1))) * 2^n * n^n / ((1 - LambertW(exp(-1))) * exp(n) * LambertW(exp(-1))^(n + 1/2)). - Vaclav Kotesovec, Jun 02 2023
MAPLE
a := n -> add(add(binomial(k, j)*(2*j + 1)^n, j=0..k)*2^(n-k), k=0..n):
seq(a(n), n = 0..17);
MATHEMATICA
Table[Sum[2^(n-k) * Sum[Binomial[k, j] * (2*j+1)^n, {j, 0, k}], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jun 02 2023 *)
CROSSREFS
Cf. A363398.
Sequence in context: A140606 A355219 A014505 * A274722 A347927 A127184
KEYWORD
nonn
AUTHOR
Peter Luschny, Jun 02 2023
STATUS
approved