A228648 -id:A228648 - cp's OEIS frontend

A231620 a(n) = A000930(n^2), where A000930 is Narayana's cows sequence.

1, 1, 3, 19, 277, 8641, 578949, 83316385, 25753389181, 17098272199297, 24382819596721629, 74684329652984094451, 491347682599497451569523, 6943240361573523613067995729, 210741152533202801182666172606913, 13738849457010997118546333815068560833, 1923823572225984354415961546862346889944243

Offset: 0

Paul D. Hanna, Nov 13 2013

nonn

G. C. Greubel, Table of n, a(n) for n = 0..75

Cf. A000930, A231621, A228647, A228648.

Table[SeriesCoefficient[1/(1 - x - x^3), {x, 0, n^2}], {n,0,25}] (* G. C. Greubel, Apr 26 2017 *)

{a(n) = polcoeff(1/(1-x-x^3 + x*O(x^(n^2))), n^2)}
for(n=0, 20, print1(a(n), ", "))

a(n) = [x^(n^2)] 1 / (1 - x - x^3) for n>=0.

A228647 a(n) = A001609(n^2) for n>=1, where g.f. of A001609 is x(1+3x^2)/(1-x-x^3).

Original entry on oeis.org

1, 5, 31, 453, 14131, 946781, 136250983, 42115660581, 27961563559891, 39874307297033165, 122134599693975367423, 803522677430288749340325, 11354589189995520431547851761, 344634362031276605039944979868611, 22467750416780812361715214948922598721, 3146114090698891414621617889648190060326821

Offset: 1

Paul D. Hanna, Aug 28 2013

nonn

A001609 forms the logarithmic derivative of Narayana's cows sequence A000930.

			L.g.f.: L(x) = x + 5*x^2/2 + 31*x^3/3 + 453*x^4/4 + 14131*x^5/5 +...
where
exp(L(x)) = 1 + x + 3*x^2 + 13*x^3 + 128*x^4 + 2974*x^5 + 161048*x^6 + 19632276*x^7 +...+ A228648(n)*x^n +...

Cf. A218439, A228648, A001609, A000930, A231620.

{A001609(n)=n*polcoeff(-log(1-x-x^3 +x*O(x^n)), n)}
{a(n)=A001609(n^2)}
for(n=1,20,print1(a(n),", "))

Equals the logarithmic derivative of A228648.

cp's OEIS Frontend

A231620 a(n) = A000930(n^2), where A000930 is Narayana's cows sequence.

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Formula

A228647 a(n) = A001609(n^2) for n>=1, where g.f. of A001609 is x(1+3x^2)/(1-x-x^3).

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Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Formula

cp's OEIS Frontend

A231620 a(n) = A000930(n^2), where A000930 is Narayana's cows sequence.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A228647 a(n) = A001609(n^2) for n>=1, where g.f. of A001609 is x*(1+3*x^2)/(1-x-x^3).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Formula

A228647 a(n) = A001609(n^2) for n>=1, where g.f. of A001609 is x(1+3x^2)/(1-x-x^3).