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 A118968 a(4n+k)=(k+1)*binomial(5n+k,n)/(4n+k+1), k=0,..3. 5
 1, 1, 1, 1, 1, 2, 3, 4, 5, 11, 18, 26, 35, 80, 136, 204, 285, 665, 1155, 1771, 2530, 5980, 10530, 16380, 23751, 56637, 100688, 158224, 231880, 556512, 996336, 1577532, 2330445, 5620485, 10116873, 16112057, 23950355, 57985070, 104819165 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Row sums of Riordan array (1,x(1-x^4))^(-1). a(4n)=A002294(n),a(4n+1)=A118969(n),a(4n+2)=A118970(n),a(4n+3)=A118971(n). LINKS FORMULA G.f. satisfies: A(x) = 1 + x*A(x)^2*A(-x)*A(I*x)*A(-I*x). - Paul D. Hanna, Jun 04 2012 G.f. satisfies: A(x) = 1 + x*A(x)*G(x^4) where G(x) = 1 + x*G(x)^5 is the g.f. of A002294. - Paul D. Hanna, Jun 04 2012 PROG (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+x*A^2*subst(A, x, -x)*subst(A, x, I*x)*subst(A, x, -I*x)); polcoeff(A, n)} \\ Paul D. Hanna, Jun 04 2012 (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*A*exp(sum(m=1, n\4, 4*polcoeff(log(A+x*O(x^n)), 4*m)*x^(4*m))+x*O(x^n))); polcoeff(A, n)} \\ Paul D. Hanna, Jun 04 2012 CROSSREFS Cf. A124753, A002294. Sequence in context: A052418 A051800 A121432 * A073528 A116067 A063685 Adjacent sequences:  A118965 A118966 A118967 * A118969 A118970 A118971 KEYWORD easy,nonn AUTHOR Paul Barry, May 07 2006 STATUS approved

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Last modified May 25 22:17 EDT 2019. Contains 323576 sequences. (Running on oeis4.)