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A264395 Number of Mersenne number parts in all partitions of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 18 04:50 EDT 2019. Contains 326072 sequences. (Running on oeis4.)