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.

A381890 Expansion of Product_{k>=1} (1 + k*x)^((1/12) * (3/4)^k).

Original entry on oeis.org

1, 1, -3, 21, -225, 3207, -56821, 1202099, -29558466, 828401462, -26068940938, 910286433318, -34930741605414, 1461245816594058, -66187658069563710, 3227353484661602866, -168557942284281821933, 9388117645333487820387, -555463036269652132509113
Offset: 0

Views

Author

Seiichi Manyama, May 26 2025

Keywords

Crossrefs

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, (-1)^(k-1)*sum(j=0, k, 3^(j-1)*j!*stirling(k, j, 2))*x^k/k)))

Formula

G.f. A(x) satisfies A(x) = (1+x)^(1/4) * A(x/(1+x))^(3/4).
G.f.: exp(Sum_{k>=1} (-1)^(k-1) * A050352(k) * x^k/k).
G.f.: 1/B(-x), where B(x) is the g.f. of A090353.

A384344 Expansion of Product_{k>=1} (1 + k*x)^((1/6) * (2/3)^k).

Original entry on oeis.org

1, 1, -2, 10, -77, 787, -9972, 150552, -2637729, 52615903, -1177590290, 29228602546, -796945212035, 23681656958269, -761803800466856, 26376749702235900, -978091742247376932, 38674335439691203644, -1624351949069462807480, 72221688529265896447384
Offset: 0

Views

Author

Seiichi Manyama, May 26 2025

Keywords

Crossrefs

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, (-1)^(k-1)*sum(j=0, k, 2^(j-1)*j!*stirling(k, j, 2))*x^k/k)))

Formula

G.f. A(x) satisfies A(x) = (1+x)^(1/3) * A(x/(1+x))^(2/3).
G.f.: exp(Sum_{k>=1} (-1)^(k-1) * A050351(k) * x^k/k).
G.f.: 1/B(-x), where B(x) is the g.f. of A090351.

A384345 Expansion of Product_{k>=1} (1 + k*x)^((1/20) * (4/5)^k).

Original entry on oeis.org

1, 1, -4, 36, -494, 9026, -205284, 5581276, -176518189, 6366839811, -257967985400, 11601382088720, -573484266103260, 30909105184132900, -1804012437852543160, 113356419526025564808, -7629831521445348113927, 547688013439312943707673, -41765446604358525581076812
Offset: 0

Views

Author

Seiichi Manyama, May 26 2025

Keywords

Crossrefs

Programs

  • PARI
    my(N=20, x='x+O('x^N)); Vec(exp(sum(k=1, N, (-1)^(k-1)*sum(j=0, k, 4^(j-1)*j!*stirling(k, j, 2))*x^k/k)))

Formula

G.f. A(x) satisfies A(x) = (1+x)^(1/5) * A(x/(1+x))^(4/5).
G.f.: exp(Sum_{k>=1} (-1)^(k-1) * A050353(k) * x^k/k).
G.f.: 1/B(-x), where B(x) is the g.f. of A090356.
Showing 1-3 of 3 results.