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A320795 Number of multisets of exactly ten partitions of positive integers into distinct parts with total sum of parts equal to n. 2
1, 1, 3, 5, 11, 19, 37, 63, 115, 195, 339, 565, 954, 1565, 2580, 4174, 6751, 10775, 17161, 27051, 42510, 66261, 102900, 158746, 243955, 372778, 567443, 859492, 1296958, 1948458, 2916636, 4348377, 6460535, 9563222, 14109242, 20744995, 30405638, 44422190 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,3

LINKS

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

FORMULA

a(n) = [x^n y^10] Product_{j>=1} 1/(1-y*x^j)^A000009(j).

MAPLE

g:= proc(n) option remember; `if`(n=0, 1, add(add(`if`(d::odd,

      d, 0), d=numtheory[divisors](j))*g(n-j), j=1..n)/n)

    end:

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

      add(b(n-i*j, i-1)*x^j*binomial(g(i)+j-1, j), j=0..n/i))), x, 11)

    end:

a:= n-> coeff(b(n$2), x, 10):

seq(a(n), n=10..60);

CROSSREFS

Column k=10 of A285229.

Cf. A000009.

Sequence in context: A320792 A320793 A320794 * A285230 A089098 A129384

Adjacent sequences:  A320792 A320793 A320794 * A320796 A320797 A320798

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 21 2018

STATUS

approved

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Last modified November 17 01:05 EST 2019. Contains 329209 sequences. (Running on oeis4.)