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A222737 Total sum of parts of multiplicity 9 in all partitions of n. 2
1, 0, 1, 1, 2, 2, 4, 4, 7, 10, 14, 16, 25, 30, 42, 53, 71, 88, 121, 148, 195, 241, 312, 384, 494, 605, 765, 943, 1179, 1441, 1796, 2181, 2694, 3273, 4011, 4849, 5922, 7130, 8652, 10398, 12552, 15021, 18072, 21558, 25816, 30729, 36649, 43480, 51705, 61163 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 9..1000

FORMULA

G.f.: (x^9/(1-x^9)^2-x^10/(1-x^10)^2)/Product_{i>=1}(1-x^i).

a(n) ~ 19 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (16200 * Pi^2). - Vaclav Kotesovec, May 29 2018

MAPLE

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

      add((l->`if`(m=9, l+[0, l[1]*p], l))(b(n-p*m, p-1)), m=0..n/p)))

    end:

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

seq(a(n), n=9..60);

MATHEMATICA

b[n_, p_] := b[n, p] = If[n == 0 && p == 0, {1, 0}, If[p == 0, Array[0&, n+2], Sum[Function[l, ReplacePart[l, m+2 -> p*l[[1]] + l[[m+2]]]][Join[b[n-p*m, p-1], Array[0&, p*m]]], {m, 0, n/p}]]]; a[n_] := b[n, n][[11]]; Table[a[n], {n, 9, 60}] (* Jean-Fran├žois Alcover, Jan 24 2014, after Alois P. Heinz *)

CROSSREFS

Column k=9 of A222730.

Sequence in context: A253412 A291148 A032190 * A005852 A274625 A292253

Adjacent sequences:  A222734 A222735 A222736 * A222738 A222739 A222740

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 03 2013

STATUS

approved

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Last modified February 26 05:51 EST 2020. Contains 332277 sequences. (Running on oeis4.)