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A102287 Total number of even blocks in all partitions of n-set. 3
0, 1, 3, 13, 55, 256, 1274, 6791, 38553, 232171, 1477355, 9898780, 69621864, 512585529, 3940556611, 31560327945, 262805569159, 2271094695388, 20333574916690, 188322882941471, 1801737999086129, 17783472151154007, 180866601699482803, 1893373126840572056 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..575

FORMULA

E.g.f: (cosh(x)-1)*exp(exp(x)-1).

EXAMPLE

a(3)=3 because in the 5 (=A000110(3)) partitions 123, (12)/3, (13)/2, 1/(23) and 1/2/3 of {1,2,3} we have 3 blocks of even size (shown between parentheses).

MAPLE

G:=(cosh(x)-1)*exp(exp(x)-1): Gser:=series(G, x=0, 28): seq(n!*coeff(Gser, x^n), n=1..25); # Emeric Deutsch, Jun 22 2005

# second Maple program:

with(combinat):

b:= proc(n, i) option remember; `if`(n=0 or i=1, [1, 0],

       add((p->(p+[0, `if`(i::odd, 0, j)*p[1]]))(

       b(n-i*j, i-1))*multinomial(n, n-i*j, i$j)/j!, j=0..n/i))

    end:

a:= n-> b(n$2)[2]:

seq(a(n), n=1..30);  # Alois P. Heinz, Sep 16 2015

MATHEMATICA

Range[0, nn]! CoefficientList[

  D[Series[Exp[y (Cosh[x] - 1) + Sinh[x]], {x, 0, nn}], y] /. y -> 1,  x]  (* Geoffrey Critzer, Aug 28 2012 *)

CROSSREFS

Cf. A005493, A000296.

Sequence in context: A151318 A151212 A151213 * A151214 A151215 A151216

Adjacent sequences:  A102284 A102285 A102286 * A102288 A102289 A102290

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Feb 19 2005

EXTENSIONS

More terms from Emeric Deutsch, Jun 22 2005

STATUS

approved

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Last modified August 8 19:29 EDT 2020. Contains 336298 sequences. (Running on oeis4.)