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A099948 Number of partitions of n such that the number of blocks is congruent to 3 mod 4. 1
1, 6, 25, 90, 302, 994, 3487, 15210, 92489, 713988, 5979480, 50184316, 412595913, 3317961318, 26241631409, 205918294518, 1622545217510, 13045429410974, 109152638729439, 969395726250226, 9255388478615017, 94973500733767432, 1034488089509527120 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..500

M. Klazar, Bell numbers, their relatives and algebraic differential equations, J. Combin. Theory, A 102 (2003), 63-87.

FORMULA

G.f.: sum(x^k/[(1-x)(1-2x)...(1-kx)], k=3 (mod 4)). - Emeric Deutsch, Dec 15 2004

EXAMPLE

a(11)=92489 because stirling2(11,3)+stirling2(11,7)+stirling2(11,11)=92489.

MAPLE

seq(sum(stirling2(n, 3+4*k), k=0..(n-3)/4), n=3..26); # Emeric Deutsch, Dec 15 2004

# second Maple program:

with(combinat):

b:= proc(n, i, m) option remember; `if`(n=0, `if`(m=3, 1, 0),

     `if`(i<1, 0, add(multinomial(n, n-i*j, i$j)/j!*

      b(n-i*j, i-1, irem(m+j, 4)), j=0..n/i)))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=3..30);  # Alois P. Heinz, Sep 17 2015

MATHEMATICA

Table[Sum[StirlingS2[n, 3+4*k], {k, 0, (n-3)/4}], {n, 3, 26}] (* Jean-Fran├žois Alcover, Feb 18 2016, after Emeric Deutsch *)

CROSSREFS

Sequence in context: A055337 A001871 A000392 * A277973 A143815 A209241

Adjacent sequences:  A099945 A099946 A099947 * A099949 A099950 A099951

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 12 2004

EXTENSIONS

More terms from Emeric Deutsch, Dec 15 2004

STATUS

approved

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Last modified July 15 14:07 EDT 2019. Contains 325030 sequences. (Running on oeis4.)