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.

A379690 Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x*exp(2*x)) ).

Original entry on oeis.org

1, 1, 8, 102, 1952, 49920, 1603392, 62100304, 2818386944, 146748098304, 8624885719040, 564885716972544, 40800979548180480, 3222148806557544448, 276214603877715378176, 25544721442331112192000, 2535168741071076287971328, 268757182971129822376624128, 30311086789573678207758237696
Offset: 0

Views

Author

Seiichi Manyama, Dec 29 2024

Keywords

Crossrefs

Cf. A379661, A379689, A379691.

Programs

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} (2*n-2*k)^k * (2*n-k)!/(k! * (n-k)!).

A379689 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(x) * (1 - x*exp(2*x)) ).

Original entry on oeis.org

1, 0, 5, 26, 557, 9504, 254737, 7405712, 264468185, 10599167744, 484155176381, 24530813822976, 1373346539948869, 83980088153710592, 5576376312266516681, 399370804845913339904, 30695207044654060184753, 2519882221014204064727040, 220076205166821624927515893
Offset: 0

Views

Author

Seiichi Manyama, Dec 29 2024

Keywords

Crossrefs

Cf. A379661, A379690, A379691.

Programs

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} (n-2*k-1)^k * (2*n-k)!/(k! * (n-k)!).

A379691 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) * (1 - x*exp(2*x)) ).

Original entry on oeis.org

1, 2, 17, 274, 6597, 212736, 8624581, 421843472, 24185705417, 1591194859264, 118184516071641, 9782950785024000, 893132377427288653, 89156432069922504704, 9661304014254414999821, 1129505503357457643206656, 141711496280128816909982097, 18992404410135723679211716608
Offset: 0

Views

Author

Seiichi Manyama, Dec 29 2024

Keywords

Crossrefs

Cf. A379661, A379689, A379690.

Programs

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

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} (3*n-2*k+1)^k * (2*n-k)!/(k! * (n-k)!).

A379662 Expansion of e.g.f. (1/x) * Series_Reversion( x * (exp(-3*x) - x) ).

Original entry on oeis.org

1, 4, 55, 1407, 53697, 2743893, 176247927, 13657260501, 1240444335969, 129281173193385, 15210977483374479, 1994549350608453609, 288445997202717914433, 45611213861740547292093, 7829287622920723803498279, 1449907335654700964735333997, 288151338120152032299063196737
Offset: 0

Views

Author

Seiichi Manyama, Dec 29 2024

Keywords

Crossrefs

Cf. A377890, A379661.

Programs

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

Formula

a(n) = n! * Sum_{k=0..n} 3^k * (2*n-k+1)^(k-1) * binomial(2*n-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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