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 1-5 of 5 results.

A385939 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + k^2) * binomial(n-1,k) * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 5, 88, 3893, 352536, 57322537, 15277686880, 6239711818377, 3708478187297920, 3079046917046731661, 3455392385954013825024, 5100835934217411940938685, 9682263835381845999967986688, 23180826149963609282826172967025, 68850271609123855250628849758027776
Offset: 0

Views

Author

Seiichi Manyama, Jul 13 2025

Keywords

Crossrefs

Programs

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

Formula

E.g.f. A(x) satisfies A(x) = exp( x * A(x) + x^2 * (d/dx A(x)) + x^3 * (d^2/dx^2 A(x)) ).

A385940 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + k^3) * binomial(n-1,k) * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 5, 148, 17189, 5676336, 4326290857, 6602349049360, 18222895109730537, 84299882148193513600, 616234715187848381357261, 6792153358905298302629935104, 108647409624774384033524243233165, 2443481854821246436998727854436139008, 75225062360951292682727255438183855480625
Offset: 0

Views

Author

Seiichi Manyama, Jul 13 2025

Keywords

Crossrefs

Programs

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

Formula

E.g.f. A(x) satisfies A(x) = exp( x*A(x) + x*Sum_{k=1..3} Stirling2(3,k) * x^k * (d^k/dx^k A(x)) ).

A385942 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + k^5) * binomial(n-1,k) * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 5, 508, 497861, 2554041696, 47918955042217, 2608995595530944320, 350836859825187730934697, 103472315352121087796983183360, 61101436986101317921145771113951181, 67212924933426575369862458525709786073344, 129898118403746997254471428114728554653243564525
Offset: 0

Views

Author

Seiichi Manyama, Jul 13 2025

Keywords

Crossrefs

Programs

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

Formula

E.g.f. A(x) satisfies A(x) = exp( x*A(x) + x*Sum_{k=1..5} Stirling2(5,k) * x^k * (d^k/dx^k A(x)) ).

A385943 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + k^6) * binomial(n-1,k) * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 5, 988, 2888933, 59194266336, 5550172939486537, 1812719786900514856960, 1706146365658760367161728617, 4025335006744077207541517795929600, 21392361120121469487882204135345762936461, 235316442953945260569915546964215106936729204224
Offset: 0

Views

Author

Seiichi Manyama, Jul 13 2025

Keywords

Crossrefs

Programs

  • PARI
    a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (1+j)*(1+j^6)*binomial(i-1, j)*v[j+1]*v[i-j])); v;

Formula

E.g.f. A(x) satisfies A(x) = exp( x*A(x) + x*Sum_{k=1..6} Stirling2(6,k) * x^k * (d^k/dx^k A(x)) ).

A386507 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * k^4 * binomial(n-1,k) * a(k) * a(n-1-k).

Original entry on oeis.org

1, 1, 3, 151, 49525, 63641021, 239036610181, 2170214958201445, 41702857906969051017, 1537709560908537888618409, 100904503302575334820438217641, 11100605398391683050596962755215561, 1950420777626865443224119613333235611309, 525796384523344023260217345195483215249534941
Offset: 0

Views

Author

Seiichi Manyama, Jul 24 2025

Keywords

Crossrefs

Programs

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

Formula

E.g.f. A(x) satisfies A(x) = exp( x + x*Sum_{k=1..4} Stirling2(4,k) * x^k * (d^k/dx^k A(x)) ).
Showing 1-5 of 5 results.