A335110 a(n) = Sum_{k=0..n} (Stirling1(n,k) mod 2) * k.

0, 1, 3, 5, 6, 8, 18, 22, 12, 14, 30, 34, 36, 40, 84, 92, 24, 26, 54, 58, 60, 64, 132, 140, 72, 76, 156, 164, 168, 176, 360, 376, 48, 50, 102, 106, 108, 112, 228, 236, 120, 124, 252, 260, 264, 272, 552, 568, 144, 148, 300, 308, 312, 320, 648, 664, 336, 344, 696, 712, 720

Offset

0,3

Links

Table of n, a(n) for n=0..60.

Formula

G.f.: x * g(x) + (3/4) * x * (1 + x) * g'(x), where g(x) = Product_{k>=0} (1 + 2 * x^(2^(k + 1))).

a(n) = floor((3*n + 1)/2) * 2^(A000120(floor(n/2)) - 1).

Mathematica

Table[Sum[Mod[StirlingS1[n, k], 2] k, {k, 0, n}], {n, 0, 60}]
Table[Floor[(3 n + 1)/2] 2^(DigitCount[Floor[n/2], 2, 1] - 1), {n, 0, 60}]

Prog

(PARI) a(n) = sum(k=0, n, (stirling(n, k, 1) % 2) * k); \\ Michel Marcus, May 23 2020

Crossrefs

Cf. A000120, A007494, A060632, A087748, A087755, A335063.

Sequence in context: A039014 A102989 A005623 * A152989 A308051 A261028

Adjacent sequences: A335107 A335108 A335109 * A335111 A335112 A335113

Keyword

nonn

Author

Ilya Gutkovskiy, May 23 2020

Status

approved