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.

A377541 E.g.f. satisfies A(x) = 1/(1 - x * exp(x*A(x)))^2.

Original entry on oeis.org

1, 2, 10, 90, 1184, 20650, 450252, 11803526, 361892848, 12712357170, 503564718260, 22212233618542, 1079909444635848, 57379354040049002, 3308238701451609772, 205715613407117613270, 13724187813695296374752, 977841609869801208944482, 74108335568947966714172004
Offset: 0

Views

Author

Seiichi Manyama, Oct 31 2024

Keywords

Crossrefs

Cf. A161633, A377545, A377551.
Cf. A364980.

Programs

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A364980.
a(n) = 2 * n! * Sum_{k=0..n} k^(n-k) * binomial(2*n-k+2,k)/( (2*n-k+2)*(n-k)! ).

A377545 E.g.f. satisfies A(x) = 1/(1 - x * exp(x*A(x)))^3.

Original entry on oeis.org

1, 3, 18, 195, 3108, 65595, 1730538, 54891165, 2036187576, 86536398195, 4147191867630, 221314773837333, 13017260705093604, 836754118106509083, 58364080427471191506, 4390560359156841730605, 354356981533262814367728, 30543768949098926368973667, 2800395449868306713606542422
Offset: 0

Views

Author

Seiichi Manyama, Oct 31 2024

Keywords

Crossrefs

Cf. A161633, A377541, A377551.
Cf. A364981.

Programs

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

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A364981.
a(n) = 3 * n! * Sum_{k=0..n} k^(n-k) * binomial(3*n-2*k+3,k)/( (3*n-2*k+3)*(n-k)! ).

A377550 E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x*A(x)^4).

Original entry on oeis.org

1, 1, 4, 45, 772, 17865, 525966, 18794881, 790175128, 38221092657, 2091074167450, 127675964340441, 8606833626646740, 634928943628432921, 50878715440232312374, 4400937219238706030865, 408700742920092110904496, 40558224679468186878237153, 4283310197644529184427059378
Offset: 0

Views

Author

Seiichi Manyama, Oct 31 2024

Keywords

Crossrefs

Cf. A161633, A364980, A364981.
Cf. A377551, A377552.

Programs

  • PARI
    a(n) = n!*sum(k=0, n, k^(n-k)*binomial(4*n-3*k+1, k)/((4*n-3*k+1)*(n-k)!));

Formula

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

A377552 E.g.f. satisfies A(x) = 1/(1 - x * exp(x*A(x)^2))^2.

Original entry on oeis.org

1, 2, 10, 114, 2000, 47050, 1399452, 50386406, 2130643216, 103530094866, 5684985037460, 348165567064942, 23530146364469208, 1739586913373486138, 139658209205202262876, 12099843726478251739830, 1125274333255817053205792, 111809642081518362872011042, 11821367007844973309548419876
Offset: 0

Views

Author

Seiichi Manyama, Oct 31 2024

Keywords

Crossrefs

Cf. A377550, A377551.

Programs

  • PARI
    a(n) = 2*n!*sum(k=0, n, k^(n-k)*binomial(4*n-3*k+2, k)/((4*n-3*k+2)*(n-k)!));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377550.
a(n) = 2 * n! * Sum_{k=0..n} k^(n-k) * binomial(4*n-3*k+2,k)/( (4*n-3*k+2)*(n-k)! ).
Showing 1-4 of 4 results.

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

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