A099948 Number of partitions of n such that the number of blocks is congruent to 3 mod 4.

1, 6, 25, 90, 302, 994, 3487, 15210, 92489, 713988, 5979480, 50184316, 412595913, 3317961318, 26241631409, 205918294518, 1622545217510, 13045429410974, 109152638729439, 969395726250226, 9255388478615017, 94973500733767432, 1034488089509527120

Offset: 3

Author

N. J. A. Sloane, Nov 12 2004

Keywords

• nonn
• easy

Examples

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

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.

Crossrefs

Cf. A143817, A358499.

Programs

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-François Alcover, Feb 18 2016, after Emeric Deutsch *)

Formula

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

Extensions

More terms from Emeric Deutsch, Dec 15 2004