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.

A379864 Expansion of e.g.f. (1/x) * Series_Reversion( x * (exp(-x) - x)^2 ).

Original entry on oeis.org

1, 4, 54, 1334, 48816, 2383682, 146036788, 10781227690, 932243805168, 92452039842626, 10346916215343564, 1290195352404492602, 177396099439904780200, 26665611450484642809058, 4350590232650155748720484, 765717105431099707449714218
Offset: 0

Views

Author

Seiichi Manyama, Jan 04 2025

Keywords

Links

Crossrefs

Cf. A379867.

Programs

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

Formula

E.g.f. A(x) satisfies A(x) = 1/(exp(-x*A(x)) - x*A(x))^2.
E.g.f.: B(x)^2, where B(x) is the e.g.f. of A379867.
a(n) = 2 * n! * Sum_{k=0..n} (3*n-k+2)^(k-1) * binomial(3*n-k+2,n-k)/k!.

A379870 E.g.f. A(x) satisfies A(x) = 1/(exp(-x*A(x)^3) - x*A(x)^3).

Original entry on oeis.org

1, 2, 31, 991, 48873, 3276921, 278486359, 28694553119, 3476833863281, 484490228040865, 76339085661865791, 13421203354104200271, 2604724304171427849145, 553128917492225243766065, 127578750880241791377948359, 31761039697155404251033218751, 8488576933611794321694363786849
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2025

Keywords

Crossrefs

Cf. A377890, A379867.

Programs

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

Formula

E.g.f.: ( (1/x) * Series_Reversion( x * (exp(-x) - x)^3 ) )^(1/3).
a(n) = n! * Sum_{k=0..n} (4*n-k+1)^(k-1) * binomial(4*n-k+1,n-k)/k!.

A379884 E.g.f. A(x) satisfies A(x) = 1/(exp(-x*A(x)^2) - x).

Original entry on oeis.org

1, 2, 15, 223, 5045, 154161, 5949715, 277816813, 15234148585, 959821848433, 68333878996991, 5425649143910733, 475370226250388221, 45559752911807595865, 4741534923025152367627, 532526268840445510805341, 64198018232238090097818065, 8268729272698380485865553761
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2025

Keywords

Crossrefs

Cf. A377892, A379867.
Cf. A088690.

Programs

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

Formula

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

A379886 E.g.f. A(x) satisfies A(x) = 1/(exp(-x) - x*A(x)^2).

Original entry on oeis.org

1, 2, 15, 247, 6221, 212421, 9181555, 480780875, 29589829785, 2093629793113, 167458531710431, 14942213260220247, 1471585837443194533, 158562898380718019813, 18555214181719160291403, 2343490814996151816116131, 317730224718816177328965425, 46028095309438150072340711601
Offset: 0

Views

Author

Seiichi Manyama, Jan 05 2025

Keywords

Crossrefs

Cf. A377891, A377893, A379867.

Programs

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

Formula

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