A264395 Number of Mersenne number parts in all partitions of n.

0, 1, 2, 5, 8, 14, 23, 37, 55, 84, 121, 175, 247, 346, 476, 654, 881, 1184, 1574, 2081, 2725, 3559, 4605, 5939, 7610, 9713, 12327, 15598, 19631, 24633, 30780, 38342, 47577, 58884, 72615, 89324, 109539, 133998, 163455, 198949, 241505, 292550, 353547, 426394

Offset

0,3

Comments

a(n) = Sum_{k=0..n} k*A264394(n,k).

Links

Table of n, a(n) for n=0..43.

Formula

G.f.: ( Sum_{i>0} x^(h(i))/(1-x^(h(i))) ) / ( Product_{i>0} 1-x^i ), where h(i) = 2^i - 1.

Example

a(4) = 8 because the partitions of 4 are [4], [3',1'], [2,2], [2,1',1'], [1',1',1',1'], where the Mersenne number parts are marked.

Maple

h := proc (i) options operator, arrow: 2^i-1 end proc: g := (sum(x^h(i)/(1-x^h(i)), i = 1..31))/(product(1-x^i, i = 1..100)); hser := series(g, x = 0, 55): seq(coeff(hser, x, n), n = 0 .. 50);

Crossrefs

Cf. A000225, A264394.

Sequence in context: A023674 A281864 A304025 * A139218 A263235 A017988

Adjacent sequences: A264392 A264393 A264394 * A264396 A264397 A264398

Keyword

nonn

Author

Emeric Deutsch, Nov 13 2015

Status

approved