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.

A364989 E.g.f. satisfies A(x) = 1 + x*A(x)^4*exp(x*A(x)^4).

Original entry on oeis.org

1, 1, 10, 207, 6628, 288885, 15969606, 1070760523, 84448152328, 7660906993737, 785932068816010, 89973000854464431, 11370915080258640204, 1572520778920744136029, 236212754707591898128270, 38299196311415039667233715, 6666717272317556205911393296
Offset: 0

Views

Author

Seiichi Manyama, Aug 15 2023

Keywords

Crossrefs

Cf. A161633, A364982, A364986.

Programs

  • PARI
    a(n) = n!*sum(k=0, n, k^(n-k)*binomial(4*n+1, k)/(n-k)!)/(4*n+1);

Formula

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

A377553 Expansion of e.g.f. (1/x) * Series_Reversion( x/(1 + x*exp(x))^2 ).

Original entry on oeis.org

1, 2, 14, 174, 3176, 77010, 2336892, 85316714, 3644408336, 178412603778, 9851421767060, 605826315779322, 41068369222584024, 3042849619010389058, 244657525386435161756, 21217387476442659806250, 1974219906922046702054432, 196191093901292764305110274, 20739322455031604846405387556
Offset: 0

Views

Author

Seiichi Manyama, Nov 01 2024

Keywords

Links

Crossrefs

Cf. A161633, A377554.
Cf. A364982.

Programs

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

Formula

E.g.f. satisfies A(x) = (1 + x * A(x) * exp(x*A(x)))^2.
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A364982.
a(n) = (n!/(n+1)) * Sum_{k=0..n} k^(n-k) * binomial(2*n+2,k)/(n-k)!.

A364986 E.g.f. satisfies A(x) = 1 + x*A(x)^3*exp(x*A(x)^3).

Original entry on oeis.org

1, 1, 8, 129, 3196, 107465, 4575966, 236120059, 14322901832, 998966928897, 78770826493210, 6929685905371691, 672900446143476156, 71491442785783506577, 8249400210035835040022, 1027394346436911560475915, 137360293432089585554830096
Offset: 0

Views

Author

Seiichi Manyama, Aug 15 2023

Keywords

Crossrefs

Cf. A364983, A364984, A364985.
Cf. A161633, A364982, A364989.
Cf. A002293.

Programs

  • PARI
    a(n) = n!*sum(k=0, n, k^(n-k)*binomial(3*n+1, k)/(n-k)!)/(3*n+1);

Formula

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

A379868 E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^2) + x*A(x)^2.

Original entry on oeis.org

1, 0, 1, -1, 25, -101, 2281, -19895, 472305, -6760297, 177126121, -3578690435, 105341330953, -2743981145933, 91092111623241, -2888769295882111, 107832291781283809, -4009180998104138321, 167254334458983887689, -7105017992715364001147, 328862774630320838523321
Offset: 0

Views

Author

Seiichi Manyama, Jan 04 2025

Keywords

Crossrefs

Cf. A108919, A379871.
Cf. A377859, A379879.
Cf. A364982, A367866.

Programs

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

Formula

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

A377549 E.g.f. satisfies A(x) = 1 + x*A(x)^5*exp(x*A(x)^2).

Original entry on oeis.org

1, 1, 12, 285, 10444, 520465, 32882406, 2519264797, 227003238792, 23526134771553, 2757165645132010, 360564513170510341, 52053350012338720332, 8222888925567102799441, 1410913077291231960911934, 261306906300110395598900685, 51955790654759866661097707536
Offset: 0

Views

Author

Seiichi Manyama, Oct 31 2024

Keywords

Crossrefs

Cf. A364980, A364982, A364985, A365176.
Cf. A377547.

Programs

  • PARI
    a(n) = n!*sum(k=0, n, k^(n-k)*binomial(2*n+3*k+1, k)/((2*n+3*k+1)*(n-k)!));

Formula

a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(2*n+3*k+1,k)/( (2*n+3*k+1)*(n-k)! ).
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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