OFFSET
0,3
COMMENTS
Row sums of A291452.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..100
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} binomial(4*n-1,4*k-1) * a(n-k). - Ilya Gutkovskiy, Jan 21 2020
MAPLE
MATHEMATICA
P[m_, n_] := P[m, n] = If[n == 0, 1, Sum[Binomial[m*n, m*k]*P[m, n - k]*x, {k, 1, n}]];
a[n_] := Module[{cl = CoefficientList[P[4, n], x]}, Sum[cl[[k + 1]]/k!, {k, 0, n}]];
PROG
(PARI) seq(n)={my(a=vector(n+1)); a[1]=1; for(n=1, n, a[1+n]=sum(k=1, n, binomial(4*n-1, 4*k-1) * a[1+n-k])); a} \\ Andrew Howroyd, Jan 21 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Sep 07 2017
STATUS
approved