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.

A377503 E.g.f. satisfies A(x) = 1/(1 - x * exp(x) * A(x))^2.

Original entry on oeis.org

1, 2, 18, 270, 5936, 173330, 6335772, 278724362, 14350790064, 847007698338, 56397332340020, 4182866692785242, 342022887565717800, 30570009715185100082, 2965368922693150575084, 310276298423966343555690, 34834957115496822249510752, 4177193847524372747798263106
Offset: 0

Views

Author

Seiichi Manyama, Oct 30 2024

Keywords

Crossrefs

Cf. A295238, A377504, A377528.
Cf. A006013, A364983.

Programs

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

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A364983.
a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(3*k+1,k)/( (k+1)*(n-k)! ).

A377504 E.g.f. satisfies A(x) = 1/(1 - x * exp(x) * A(x))^3.

Original entry on oeis.org

1, 3, 36, 735, 21972, 871995, 43308378, 2588123811, 180990517032, 14507325973395, 1311719669172750, 132102208441613883, 14666354372331521676, 1779817542971018697003, 234399632982398657764578, 33297612755940733707395955, 5075234637265322738651060688, 826215756199826873368252279971
Offset: 0

Views

Author

Seiichi Manyama, Oct 30 2024

Keywords

Crossrefs

Cf. A295238, A377503, A377528.
Cf. A006632, A364987.

Programs

  • PARI
    a(n) = n!*sum(k=0, n, k^(n-k)*binomial(4*k+2, k)/((k+1)*(n-k)!));

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A364987.
a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(4*k+2,k)/( (k+1)*(n-k)! ).

A377527 E.g.f. satisfies A(x) = 1/(1 - x * exp(x) * A(x)^2)^2.

Original entry on oeis.org

1, 2, 26, 618, 22256, 1081770, 66401532, 4931389358, 430108545680, 43104305664594, 4881518010253460, 616559703960596022, 85935621525038617752, 13102417265843584412474, 2169337115977056447577820, 387609934848899388554651550, 74340899731294447790784890912
Offset: 0

Views

Author

Seiichi Manyama, Oct 30 2024

Keywords

Crossrefs

Cf. A377526, A377528.
Cf. A377503, A377529.

Programs

  • PARI
    a(n) = n!*sum(k=0, n, k^(n-k)*binomial(5*k+1, k)/((2*k+1)*(n-k)!));

Formula

E.g.f.: B(x)^2, where B(x) is the e.g.f. of A377526.
a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(5*k+1,k)/( (2*k+1)*(n-k)! ).

A377744 E.g.f. satisfies A(x) = exp(x) / (1 - x * A(x))^4.

Original entry on oeis.org

1, 5, 69, 1741, 65025, 3238401, 202252549, 15216086789, 1340493558497, 135418524663457, 15436319894361141, 1960277599669850517, 274474966233168968353, 42012725272366653895169, 6979546631782182590117189, 1250777360824265136694022341, 240516661686854988775792192833
Offset: 0

Views

Author

Seiichi Manyama, Nov 06 2024

Keywords

Crossrefs

Cf. A194471, A377742, A377743.
Cf. A377528.

Programs

  • PARI
    a(n) = n!*sum(k=0, n, (k+1)^(n-k-1)*binomial(5*k+3, k)/(n-k)!);

Formula

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