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A222738 Total sum of parts of multiplicity 10 in all partitions of n. 2
1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 14, 16, 23, 28, 40, 49, 67, 82, 110, 135, 180, 220, 286, 349, 448, 548, 694, 846, 1061, 1290, 1608, 1948, 2406, 2909, 3566, 4300, 5242, 6298, 7637, 9149, 11044, 13189, 15847, 18872, 22582, 26817, 31967, 37858, 44970, 53116, 62894 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 10..1000

FORMULA

G.f.: (x^10/(1-x^10)^2-x^11/(1-x^11)^2)/Product_{i>=1}(1-x^i).

a(n) ~ 21 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (24200 * 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=10, 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=10..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][[12]]; Table[a[n], {n, 10, 60}] (* Jean-Fran├žois Alcover, Jan 24 2014, after Alois P. Heinz *)

CROSSREFS

Column k=10 of A222730.

Sequence in context: A183567 A222710 A032278 * A005308 A151532 A056503

Adjacent sequences:  A222735 A222736 A222737 * A222739 A222740 A222741

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Mar 03 2013

STATUS

approved

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Last modified January 24 19:19 EST 2020. Contains 331211 sequences. (Running on oeis4.)