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 1-3 of 3 results.

A380781 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * (1 + x)^2) / (1 + x)^2 ).

Original entry on oeis.org

1, 3, 29, 514, 13473, 470616, 20607781, 1086800352, 67105960641, 4750972007680, 379512594172941, 33771911612182272, 3313441417839023521, 355371388642280715264, 41365962922892138767125, 5193995331631149377867776, 699785874809076112607739009, 100701968551637581411176480768
Offset: 0

Views

Author

Seiichi Manyama, Feb 02 2025

Keywords

Crossrefs

Programs

  • PARI
    a(n, q=1, r=1, s=1, t=2, u=2) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial(r*u*n+((s-r)*u+t)*k+q*u, n-k)/k!);

Formula

E.g.f. A(x) satisfies A(x) = exp( x * A(x) * (1 + x*A(x))^2 ) * (1 + x*A(x))^2.
a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(2*n+2*k+2,n-k)/k!.

A380779 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x / (1 + x)) / (1 + x)^2 ).

Original entry on oeis.org

1, 3, 23, 298, 5529, 134496, 4062631, 146903184, 6193969137, 298577002240, 16204658051031, 978156957629952, 65017249611283657, 4719532271850590208, 371519503997940966375, 31526820740816885549056, 2869134152226896957509089, 278763390556764407051452416
Offset: 0

Views

Author

Seiichi Manyama, Feb 02 2025

Keywords

Crossrefs

Programs

  • PARI
    a(n, q=1, r=1, s=1, t=-1, u=2) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial(r*u*n+((s-r)*u+t)*k+q*u, n-k)/k!);

Formula

E.g.f. A(x) satisfies A(x) = exp( x * A(x) / (1 + x*A(x)) ) * (1 + x*A(x))^2.
a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(2*n-k+2,n-k)/k!.

A380780 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * (1 + x)) / (1 + x)^2 ).

Original entry on oeis.org

1, 3, 27, 436, 10353, 326856, 12920731, 614694816, 34223383809, 2184028353280, 157223422977531, 12606338448248832, 1114292924502666673, 107657947282494206976, 11287975339133863810875, 1276603658863119005618176, 154909721707963344338403969, 20076669149268201122957819904
Offset: 0

Views

Author

Seiichi Manyama, Feb 02 2025

Keywords

Crossrefs

Programs

  • PARI
    a(n, q=1, r=1, s=1, t=1, u=2) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial(r*u*n+((s-r)*u+t)*k+q*u, n-k)/k!);

Formula

E.g.f. A(x) satisfies A(x) = exp( x * A(x) * (1 + x*A(x)) ) * (1 + x*A(x))^2.
a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(2*n+k+2,n-k)/k!.
Showing 1-3 of 3 results.