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A161407 Number of partitions of n^2 into parts smaller than n. 5
1, 0, 1, 5, 30, 185, 1226, 8442, 60289, 442089, 3314203, 25295011, 195990980, 1538069121, 12203218743, 97746332667, 789480879664, 6423539487002, 52607252796831, 433368610079872, 3588859890833443, 29862449600982149, 249560820679038935, 2093852201126089073 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..320

EXAMPLE

a(3) = #{2+2+2+2+1, 2+2+2+1+1+1, 2+2+5x1, 2+7x1, 9x1} = 5.

MAPLE

a := proc (n) local G, Gser: G := 1/(product(1-x^j, j = 1 .. n-1)): Gser := series(G, x = 0, n^2+5): coeff(Gser, x, n^2) end proc: 1, seq(a(n), n = 1 .. 23); # Emeric Deutsch, Jun 20 2009

# second Maple program:

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

     `if`(i<1, 0, b(n, i-1)+`if`(i>n, 0, b(n-i, i))))

    end:

a:= n-> b(n^2, n-1):

seq(a(n), n=0..30);  # Alois P. Heinz, Dec 21 2014

MATHEMATICA

b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1] + If[i>n, 0, b[n-i, i]]]]; a[n_] := b[n^2, n-1]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Jun 30 2015, after Alois P. Heinz *)

CROSSREFS

Cf. A072213, A093115, A109655, A161408.

Sequence in context: A147837 A076036 A195257 * A006773 A059273 A038744

Adjacent sequences:  A161404 A161405 A161406 * A161408 A161409 A161410

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jun 10 2009

EXTENSIONS

More terms from Emeric Deutsch, Jun 20 2009

a(0)=1 from Alois P. Heinz, Dec 21 2014

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)