A211971 Column 0 of square array A211970 (in which column 1 is A000041).

1, 1, 2, 4, 6, 10, 16, 24, 36, 54, 78, 112, 160, 224, 312, 432, 590, 802, 1084, 1452, 1936, 2568, 3384, 4440, 5800, 7538, 9758, 12584, 16160, 20680, 26376, 33520, 42468, 53644, 67552, 84832, 106246, 132706, 165344, 205512, 254824, 315256, 389168, 479368

Offset

0,3

Comments

Partial sums give A015128. - Omar E. Pol, Jan 09 2014

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

a(n) ~ exp(Pi*sqrt(n))*Pi / (16*n^(3/2)) * (1 - (3/Pi + Pi/4)/sqrt(n) + (3/2 + 3/Pi^2+ Pi^2/24)/n). - Vaclav Kotesovec, Oct 25 2016, extended Nov 04 2016

G.f.: (1 - x)/theta_4(x), where theta_4() is the Jacobi theta function. - Ilya Gutkovskiy, Mar 05 2018

Mathematica

Flatten[{1, Differences[Table[Sum[PartitionsP[n-k]*PartitionsQ[k], {k, 0, n}], {n, 0, 60}]]}] (* Vaclav Kotesovec, Oct 25 2016 *)
CoefficientList[Series[(1 - x)/EllipticTheta[4, 0, x], {x, 0, 43}], x] (* Robert G. Wilson v, Mar 06 2018 *)

Prog

(GW-BASIC)' A program with two A-numbers:
10 Dim A008794(100), A057077(100), a(100): a(0)=1
20 For n = 1 to 43: For j = 1 to n
30 If A008794(j+1) <= n then a(n) = a(n) + A057077(j-1)*a(n - A008794(j+1))
40 Next j: Print a(n-1); : Next n

Crossrefs

Cf. A000041, A006950, A008794, A036820, A057077, A195152, A195848, A195849, A195850, A195851, A195852, A196933, A195825, A210964, A277643.

Sequence in context: A132002 A098151 A137414 * A305498 A028445 A006305

Adjacent sequences: A211968 A211969 A211970 * A211972 A211973 A211974

Keyword

nonn

Author

Omar E. Pol, Jun 10 2012

Status

approved