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 1-2 of 2 results.

A377687 E.g.f. satisfies A(x) = 1 - x*log(1 - x*A(x)^3).

Original entry on oeis.org

1, 0, 2, 3, 80, 570, 12744, 198660, 4969152, 119968128, 3607836480, 115031711520, 4163170478400, 162622297300320, 6952158785424384, 319741032356928000, 15818989359665802240, 835755271882288128000, 47015148988105365288960, 2804276310235518168161280
Offset: 0

Views

Author

Seiichi Manyama, Nov 04 2024

Keywords

Crossrefs

Cf. A371227, A377690.

Programs

  • PARI
    a(n) = n!*sum(k=0, n\2, (3*n-3*k)!*abs(stirling(n-k, k, 1))/((n-k)!*(3*n-4*k+1)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (3*n-3*k)! * |Stirling1(n-k,k)|/( (n-k)! * (3*n-4*k+1)! ).

A377689 E.g.f. satisfies A(x) = (1 + x * (exp(x*A(x)) - 1))^3.

Original entry on oeis.org

1, 0, 6, 9, 300, 1995, 48438, 720111, 17965944, 422161011, 12234150930, 380328463383, 13151800946628, 497667965729259, 20320277028840558, 899482574279597535, 42525760204244934768, 2153233176660303831267, 115738033009558749725610, 6600044862098481204272487
Offset: 0

Views

Author

Seiichi Manyama, Nov 04 2024

Keywords

Crossrefs

Cf. A371115, A377688.
Cf. A377690.

Programs

  • PARI
    a(n) = 3*n!*sum(k=0, n\2, (3*n-3*k+2)!*stirling(n-k, k, 2)/((n-k)!*(3*n-4*k+3)!));

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A377690.
a(n) = 3 * n! * Sum_{k=0..floor(n/2)} (3*n-3*k+2)! * Stirling2(n-k,k)/( (n-k)! * (3*n-4*k+3)! ).
Showing 1-2 of 2 results.

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

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