cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-14 of 14 results.

A320792 Number of multisets of exactly seven partitions of positive integers into distinct parts with total sum of parts equal to n.

Original entry on oeis.org

1, 1, 3, 5, 11, 19, 37, 63, 114, 192, 331, 547, 914, 1482, 2412, 3847, 6126, 9620, 15052, 23292, 35889, 54806, 83294, 125658, 188656, 281418, 417828, 616838, 906516, 1325457, 1929644, 2796189, 4035315, 5798648, 8300214, 11833892, 16810048, 23790327, 33552202
Offset: 7

Views

Author

Alois P. Heinz, Oct 21 2018

Keywords

Links

Crossrefs

Column k=7 of A285229.
Cf. A000009.

Programs

  • 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, 8)
    end:
a:= n-> coeff(b(n$2), x, 7):
seq(a(n), n=7..60);

Formula

a(n) = [x^n y^7] Product_{j>=1} 1/(1-y*x^j)^A000009(j).

A320793 Number of multisets of exactly eight partitions of positive integers into distinct parts with total sum of parts equal to n.

Original entry on oeis.org

1, 1, 3, 5, 11, 19, 37, 63, 115, 194, 336, 558, 938, 1530, 2508, 4030, 6472, 10246, 16179, 25270, 39325, 60664, 93187, 142119, 215800, 325647, 489288, 731154, 1087981, 1611036, 2375905, 3488306, 5101755, 7430869, 10783473, 15589092, 22457429, 32236645
Offset: 8

Views

Author

Alois P. Heinz, Oct 21 2018

Keywords

Links

Crossrefs

Column k=8 of A285229.
Cf. A000009.

Programs

  • 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, 9)
    end:
a:= n-> coeff(b(n$2), x, 8):
seq(a(n), n=8..60);

Formula

a(n) = [x^n y^8] Product_{j>=1} 1/(1-y*x^j)^A000009(j).

A320794 Number of multisets of exactly nine partitions of positive integers into distinct parts with total sum of parts equal to n.

Original entry on oeis.org

1, 1, 3, 5, 11, 19, 37, 63, 115, 195, 338, 563, 949, 1554, 2556, 4126, 6655, 10592, 16815, 26415, 41354, 64212, 99295, 152512, 233279, 354729, 537193, 809347, 1214485, 1814052, 2699197, 3999366, 5904074, 8682185, 12722807, 18576815, 27034032, 39208697
Offset: 9

Views

Author

Alois P. Heinz, Oct 21 2018

Keywords

Links

Crossrefs

Column k=9 of A285229.
Cf. A000009.

Programs

  • 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, 10)
    end:
a:= n-> coeff(b(n$2), x, 9):
seq(a(n), n=9..60);

Formula

a(n) = [x^n y^9] Product_{j>=1} 1/(1-y*x^j)^A000009(j).

A320795 Number of multisets of exactly ten partitions of positive integers into distinct parts with total sum of parts equal to n.

Original entry on oeis.org

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
Offset: 10

Views

Author

Alois P. Heinz, Oct 21 2018

Keywords

Links

Crossrefs

Column k=10 of A285229.
Cf. A000009.

Programs

  • 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);

Formula

a(n) = [x^n y^10] Product_{j>=1} 1/(1-y*x^j)^A000009(j).
Previous Showing 11-14 of 14 results.

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