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.

A383231 Expansion of e.g.f. f(x) * log(f(x)), where f(x) = 1/(1 - 5*x)^(1/5).

Original entry on oeis.org

0, 1, 7, 83, 1394, 30330, 810756, 25710012, 943434288, 39324264624, 1835297984160, 94813760519136, 5371462318747392, 331125138305434368, 22065681276731119104, 1580617232453691210240, 121117633854691036502016, 9885823380533972300470272, 856279708828545483688808448
Offset: 0

Views

Author

Seiichi Manyama, Apr 20 2025

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, k*5^(n-k)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=1..n} k * 5^(n-k) * |Stirling1(n,k)|.
a(n) = 5^(n-1) * n! * Sum_{k=0..n-1} (-1)^k * binomial(-1/5,k)/(n-k).
a(n) = (10*n-13) * a(n-1) - (5*n-9)^2 * a(n-2) for n > 1.

A383232 Expansion of e.g.f. f(x)^2 * log(f(x)), where f(x) = 1/(1 - 5*x)^(1/5).

Original entry on oeis.org

0, 1, 9, 122, 2242, 52180, 1471692, 48790608, 1859539344, 80109265824, 3849497255520, 204138860091264, 11842095171021696, 745962168915065088, 50708105952635996928, 3699802551156676392960, 288399758863879774476288, 23919432333548949807869952, 2103184085769044913951461376
Offset: 0

Views

Author

Seiichi Manyama, Apr 20 2025

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, k*2^(k-1)*5^(n-k)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=1..n} k * 2^(k-1) * 5^(n-k) * |Stirling1(n,k)|.
a(n) = 5^(n-1) * n! * Sum_{k=0..n-1} (-1)^k * binomial(-2/5,k)/(n-k).
a(n) = (10*n-11) * a(n-1) - (5*n-8)^2 * a(n-2) for n > 1.

A383234 Expansion of e.g.f. f(x)^4 * log(f(x)), where f(x) = 1/(1 - 5*x)^(1/5).

Original entry on oeis.org

0, 1, 13, 218, 4646, 121080, 3741144, 133863792, 5447294352, 248518603584, 12566268267840, 697632464382336, 42189230206182528, 2760816706845539328, 194381535085933095936, 14652311175996819978240, 1177370323796943823325184, 100466288729505689717809152
Offset: 0

Views

Author

Seiichi Manyama, Apr 20 2025

Keywords

Crossrefs

Programs

  • PARI
    a(n) = sum(k=1, n, k*4^(k-1)*5^(n-k)*abs(stirling(n, k, 1)));

Formula

a(n) = Sum_{k=1..n} k * 4^(k-1) * 5^(n-k) * |Stirling1(n,k)|.
a(n) = 5^(n-1) * n! * Sum_{k=0..n-1} (-1)^k * binomial(-4/5,k)/(n-k).
a(n) = (10*n-7) * a(n-1) - (5*n-6)^2 * a(n-2) for n > 1.
Showing 1-3 of 3 results.