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.

Showing 1-4 of 4 results.

A385843 a(n) = 1 + Sum_{k=0..n-1} k^5 * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 2, 66, 16105, 16507753, 51603272051, 401318681776723, 6745364508844808841, 221038850400001766938953, 13052344129663319516736911260, 1305247465753403752473945799113276, 210212714880649951675343095297590137757, 52307860484508916277278208388919504757392477
Offset: 0

Views

Author

Seiichi Manyama, Jul 09 2025

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, j^5*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( (1 - x) * ( 1 - x*Sum_{k=1..5} Stirling2(5,k) * x^k * (d^k/dx^k A(x)) ) ).

A385840 a(n) = 1 + Sum_{k=0..n-1} k^2 * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 2, 10, 101, 1733, 45303, 1680907, 84166419, 5475072843, 449157456364, 45377436182152, 5537042709272831, 802969519178558759, 136516626968319610486, 26895468447194766859402, 6078661245454015521843883, 1562271796018872884111521763, 453071380100390505646644605866
Offset: 0

Views

Author

Seiichi Manyama, Jul 09 2025

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, j^2*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( (1 - x) * ( 1 - x^2 * (d/dx A(x)) - x^3 * (d^2/dx^2 A(x)) ) ).

A385841 a(n) = 1 + Sum_{k=0..n-1} k^3 * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 2, 18, 505, 32857, 4141211, 898723027, 309170208201, 158606268801081, 115783226426053396, 115899337245305115516, 154378153899481307826141, 266920063540268509322880013, 586690612016923635703423527652, 1610466268575965949949881680290412
Offset: 0

Views

Author

Seiichi Manyama, Jul 09 2025

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, j^3*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( (1 - x) * ( 1 - x*Sum_{k=1..3} Stirling2(3,k) * x^k * (d^k/dx^k A(x)) ) ).

A385876 a(n) = 1 + Sum_{k=0..n-1} binomial(k+3,4) * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 2, 12, 193, 6968, 495189, 62906143, 13274340034, 4393943557987, 2179423896462618, 1560476564415661780, 1563601961040080858376, 2135883440687340361131857, 3889446901597262416621276499, 9260777373178278371280728311304, 28347247357191779349093896687278933
Offset: 0

Views

Author

Seiichi Manyama, Jul 11 2025

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, binomial(j+3, 4)*v[j+1]*v[i-j])); v;

Formula

G.f. A(x) satisfies A(x) = 1/( (1 - x) * ( 1 - x*Sum_{k=1..4} binomial(3,k-1) * x^k/k! * (d^k/dx^k A(x)) ) ).
Showing 1-4 of 4 results.