A350147 a(n) = Sum_{k=1..n} floor(n/(2*k-1))^k.

1, 2, 4, 5, 7, 11, 13, 14, 21, 29, 31, 39, 41, 57, 87, 88, 90, 133, 135, 173, 253, 317, 319, 335, 398, 526, 756, 932, 934, 1300, 1302, 1303, 1991, 2503, 3001, 3806, 3808, 4832, 6918, 7088, 7090, 9836, 9838, 13206, 21860, 25956, 25958, 25990, 27097, 35560, 54766

Offset

1,2

Links

Table of n, a(n) for n=1..51.

Formula

G.f.: (1/(1 - x)) * Sum_{j>=1} Sum{k>=1} k^j * x^(k*(2*j-1)) * (1 - x^(2*j-1)).

Limit_{n->infinity} a(n)^(1/n) = exp(exp(-1)/2). - Vaclav Kotesovec, Dec 17 2021

Mathematica

a[n_] := Sum[Floor[n/(2*k - 1)]^k, {k, 1, n}]; Array[a, 50] (* Amiram Eldar, Dec 17 2021 *)

Prog

(PARI) a(n) = sum(k=1, n, (n\(2*k-1))^k);
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(j=1, N, (1-x^(2*j-1))*sum(k=1, N, k^j*x^(k*(2*j-1))))/(1-x))

Crossrefs

Cf. A345176, A350145.

Sequence in context: A056527 A147991 A033160 * A110924 A335402 A192590

Adjacent sequences: A350144 A350145 A350146 * A350148 A350149 A350150

Keyword

nonn

Author

Seiichi Manyama, Dec 16 2021

Status

approved