A233969 Partial sums of A006950.

1, 2, 3, 5, 8, 12, 17, 24, 34, 47, 63, 84, 112, 147, 190, 245, 315, 401, 506, 636, 797, 993, 1229, 1516, 1866, 2286, 2787, 3389, 4111, 4969, 5985, 7191, 8622, 10309, 12290, 14621, 17362, 20568, 24308, 28676, 33772, 39694, 46562, 54529, 63762, 74432, 86738

Offset

0,2

Comments

The first three columns of A211970 are A211971, A000041, A006950, so for k = 0..2, the partial sums of column k of A211970 give: A015128, A000070, this sequence.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ exp(Pi*sqrt(n/2))/(2*Pi*sqrt(n)). - Vaclav Kotesovec, Oct 27 2016

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1)+`if`(i>n, 0, b(n-i, i-irem(i, 2)))))
    end:
a:= proc(n) option remember; b(n, n) +`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..50);  # Alois P. Heinz, Jan 12 2014

Mathematica

Accumulate[CoefficientList[Series[x*QPochhammer[-1/x, x^2]/((1 + x) * QPochhammer[x^2]), {x, 0, 50}], x]] (* Vaclav Kotesovec, Oct 27 2016 *)

Crossrefs

Cf. A000041, A000070, A015128, A195825, A195826, A195836, A210843, A211970, A211971, A233758, A233759.

Sequence in context: A175827 A061535 A280276 * A240202 A235945 A129504

Adjacent sequences: A233966 A233967 A233968 * A233970 A233971 A233972

Keyword

nonn

Author

Omar E. Pol, Jan 12 2014

Status

approved