A389688 Expansion of e.g.f. exp(x*cosh(x) + x^2*sinh(x)/2).

1, 1, 1, 7, 25, 76, 571, 3074, 16521, 139528, 964021, 7372432, 69668809, 589423784, 5688394167, 59670313096, 602416804369, 6826049816704, 79270834221577, 931546992774848, 11878028938404441, 152607796955122048, 2035401009469814515, 28539773642721779968, 404587078621516340185, 5987888623451494875776

Offset

0,4

Comments

Number of ways to choose one or two elements from each block of the partitions of an n-set into odd blocks.

Links

Table of n, a(n) for n=0..25.

Example

a(6) = 571 since we have (number of partitions given by A003724; (n_i,.,n_k;N) means choose n_i elements from block i,.., choose n_k elements from block k, N ways for such case):
  2 blocks: {12345} {6}: 6 such partitions, 90 ways considering the 2 cases (1,1;30), (2,1;60);
  2 blocks: {123} {456}: 10 such partitions, 360 ways considering the 4 cases (1,1;90), (1,2;90), (2,1;90), (2,2;90).
  4 blocks: {123} {4} {5} {6}: 20 such partitions, 120 ways considering the 2 cases (1,1,1,1;60), (2,1,1,1;60);
  6 blocks: {1} {2} {3} {4} {5} {6}: 1 partition, 1 way considering the single case (1,1,1,1,1,1;1).
The number of partitions is A003724(6) = 37 and the number of ways is a(6) = 571.

Crossrefs

Cf. A003724, A003727, A389224.

Sequence in context: A155281 A155254 A155295 * A168589 A058481 A220387

Adjacent sequences: A389685 A389686 A389687 * A389689 A389690 A389691

Keyword

nonn

Author

Enrique Navarrete, Oct 10 2025

Status

approved