The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A182951 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A182951

G.f.: 1/(1-x) = Sum_{n>=0} a(n)*x^n/(1+x)^(n^2+n).
(history; published version)

#7 by Andrey Zabolotskiy at Sat Mar 12 13:20:44 EST 2022

STATUS

editing

approved

#6 by Andrey Zabolotskiy at Sat Mar 12 13:20:37 EST 2022

NAME

G.f.: 1/(1-x) = Sum_{n>=0} a(n)*x^n/(1+x)^(n^2+n).

FORMULA

a(n) = 1 - Sum_{k=0..n-1} a(k)*(-1)^(n-k)*C(k^2+k + n-k-1, n-k) for n>0, with a(0)=1.

EXAMPLE

1/(1-x) = 1 + x/(1+x)^2 + 3*x^2/(1+x)^6 + 16*x^3/(1+x)^12 + 134*x^4/(1+x)^20 +...

PROG

(PARI) {a(n)=if(n==0, 1, polcoeff(-(1-x)*sum(m=0, n-1, a(m)*x^m/(1+x +x*O(x^n))^(m*(m+1))), n))}

CROSSREFS

Cf. A182952, A133316, A141761.

STATUS

approved

editing

#5 by Russ Cox at Fri Mar 30 18:37:23 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Dec 31 2010

Discussion

Fri Mar 30

18:37

OEIS Server: https://oeis.org/edit/global/213

#4 by T. D. Noe at Fri Dec 31 12:39:33 EST 2010

STATUS

proposed

approved

#3 by Paul D. Hanna at Fri Dec 31 10:35:43 EST 2010

NAME

allocated for Paul D. Hanna

G.f.: 1/(1-x) = Sum_{n>=0} a(n)*x^n/(1+x)^(n^2+n).

DATA

1, 1, 3, 16, 134, 1596, 25193, 501236, 12118038, 346373740, 11460810227, 431732603292, 18269225018646, 858920382899880, 44455946598501069, 2513531512113074244, 154218539815668325502, 10209332972405039928876

OFFSET

0,3

FORMULA

a(n) = 1 - Sum_{k=0..n-1} a(k)*(-1)^(n-k)*C(k^2+k + n-k-1, n-k) for n>0, with a(0)=1.

EXAMPLE

1/(1-x) = 1 + x/(1+x)^2 + 3*x^2/(1+x)^6 + 16*x^3/(1+x)^12 + 134*x^4/(1+x)^20 +...

PROG

(PARI) {a(n)=if(n==0, 1, polcoeff(-(1-x)*sum(m=0, n-1, a(m)*x^m/(1+x +x*O(x^n))^(m*(m+1))), n))}

(PARI) {a(n)=if(n==0, 1, 1 - sum(j=0, n-1, a(j)*(-1)^(n-j)*binomial(j*(j+1)+n-j-1, n-j)))}

CROSSREFS

Cf. A182952, A133316, A141761.

KEYWORD

allocated

nonn

AUTHOR

Paul D. Hanna (pauldhanna(AT)juno.com), Dec 31 2010

STATUS

approved

proposed

#2 by Paul D. Hanna at Wed Dec 15 21:20:24 EST 2010

KEYWORD

allocating

allocated

#1 by Paul D. Hanna at Wed Dec 15 21:20:24 EST 2010

NAME

allocated for Paul D. Hanna

KEYWORD

allocating

STATUS

approved