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 1-3 of 3 results.

A380308 Expansion of e.g.f. exp( 1 - 1/(1-2*x)^(1/2) ).

Original entry on oeis.org

1, -1, -2, -7, -35, -226, -1769, -16003, -159998, -1669645, -16203509, -85724926, 2606965153, 154547040023, 6047755681150, 217270016433329, 7721994442008061, 279057037146008702, 10378357435103977207, 399487271346562859045, 15957215240554330744066
Offset: 0

Views

Author

Seiichi Manyama, Jan 20 2025

Keywords

Links

Crossrefs

Cf. A145561, A380309, A380310.
Cf. A000587, A001147.

Programs

  • PARI
    my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(1-1/(1-2*x)^(1/2))))

Formula

a(n) = Sum_{k=0..n} 2^(n-k) * |Stirling1(n,k)| * A000587(k).
a(n) = e * (-2)^n * n! * Sum_{k>=0} (-1)^k * binomial(-k/2,n)/k!.
a(0) = 1; a(n) = -Sum_{k=1..n} A001147(k) * binomial(n-1,k-1) * a(n-k).

A380309 Expansion of e.g.f. exp( 1 - 1/(1-3*x)^(1/3) ).

Original entry on oeis.org

1, -1, -3, -17, -143, -1601, -22419, -377217, -7415743, -166854657, -4229195779, -119251176881, -3702809175823, -125546570425537, -4615357640315603, -182855338776726561, -7766868454872857599, -352082642456714366977, -16965451818345573907843
Offset: 0

Views

Author

Seiichi Manyama, Jan 20 2025

Keywords

Links

Crossrefs

Cf. A145561, A380308, A380310.
Cf. A000587, A007559, A015735.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(1-1/(1-3*x)^(1/3))))

Formula

a(n) = Sum_{k=0..n} 3^(n-k) * |Stirling1(n,k)| * A000587(k).
a(n) = e * (-3)^n * n! * Sum_{k>=0} (-1)^k * binomial(-k/3,n)/k!.
a(0) = 1; a(n) = -Sum_{k=1..n} A007559(k) * binomial(n-1,k-1) * a(n-k).

A380310 Expansion of e.g.f. exp( 1 - 1/(1-5*x)^(1/5) ).

Original entry on oeis.org

1, -1, -5, -49, -719, -14077, -344909, -10152829, -349045535, -13727327833, -607873987637, -29931556660105, -1622308999459631, -95982568510668373, -6155361624644676989, -425321834949751148053, -31502433469012320013631, -2489898822489054343250737, -209178052238110675644666341
Offset: 0

Views

Author

Seiichi Manyama, Jan 20 2025

Keywords

Links

Crossrefs

Cf. A145561, A380308, A380309.
Cf. A000587, A008548, A028575.

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(1-1/(1-5*x)^(1/5))))

Formula

a(n) = Sum_{k=0..n} 5^(n-k) * |Stirling1(n,k)| * A000587(k).
a(n) = e * (-5)^n * n! * Sum_{k>=0} (-1)^k * binomial(-k/5,n)/k!.
a(0) = 1; a(n) = -Sum_{k=1..n} A008548(k) * binomial(n-1,k-1) * a(n-k).
Showing 1-3 of 3 results.

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

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